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### Week 1: Think Again III: How to Reason Inductively Coursera Quiz Answers

#### Quiz 1: What Is Induction?

Q1. Deductive arguments are always valid.

- True
**False**

Q2. Deductive validity comes in degrees.

- True
**False**

Q3. Inductive strength comes in degrees.

**True**- False

Q4. Deductive validity is defeasible.

- True
**False**

Q5. Inductive strength is defeasible.

**True**- False

Q6. Inductive arguments always have general conclusions.

- True
**False**

Q7. Deductive arguments always provide more reason for their conclusions than inductive arguments do.

- True
**False**

Q8. INSTRUCTIONS for Exercises 8 – 12: Indicate whether each of the following arguments is deductive or inductive. Assume a standard context as described. Nothing tricky!

Context: You and I want to go for a walk, but it is raining, and we do not want to walk in the rain. You ask me when I think it will stop raining. Then I say this sentence:

“The sun is coming out, so the rain will probably stop soon.”

- Deductive
**Inductive**

Q9. Context: Harold is accused of a burglary, but we know him and thought he was a nice person, so we do not know whether to believe that he is guilty. Then you give this argument.

“If Harold were innocent, then he would not go into hiding. Since he is hiding, he must not be innocent.”

**Deductive**- Inductive

Q10. Context: Harold is accused of a burglary. We think that he is not guilty, but we worry that he might be punished anyway. Then I give this argument.

“If Harold is not innocent, then he will be punished. But he is innocent, so he will not be punished.”

**Deductive**- Inductive

Q11. Context: I order a cola drink at midnight. You comment that you never drink cola that late at night, because the caffeine in cola keeps you from sleeping well. I respond with this argument.

“Cola drinks never keep me awake at night. I know because I drank a cola drink just last night without any problems.”

- Deductive
**Inductive**

Q12. Context: Our only son, Jeff, lives away at college. He has final exams before the winter holidays, and we are not sure when he will arrive back home. We go on a short trip to a store. The house was neat when we left, but it is messy when we return. Then you say this sentence.

“The house is a mess, so Jeff must be home from college.”

- Deductive
**Inductive**

#### Quiz 2: Generalizations from Samples

Q1. Arguments from premises about a sample to conclusions about the whole class are valid.

- True
**False**

Q2. Arguments from premises about a sample to conclusions about the whole class are defeasible.

**True**- False

Q3. Arguments from premises about a sample to conclusions about the whole class are inductive.

**True**- False

Q4. The conclusion in a generalization from a sample always begins with the word “all”.

- True
**False**

Q5. Statistics are irrefutable.

- True
**False**

#### Quiz 3: When are Generalizations Strong?

Q1. Suppose I argue that 90% of Fs in my sample are G, so 90% of all Fs are G. Then I observe more Fs in a different area and find that 90% of Fs in my new sample are also G. This new information makes my argument stronger than it was before.

**True**- False

Q2. A sample of one is always too small to justify a generalization.

- True
**False**

Q3. Arguments from premises about a sample to general conclusions about the whole class commit the fallacy of hasty generalization when the sample in the premises is biased.

- True
**False**

Q4. Polls are always reliable.

- True
**False**

Q5. Polls are never reliable.

- True
**False**

Q6. When a poll asks a question that is slanted in order to reach a certain result, then the poll does not provide strong reason to believe the desired conclusion.

**True**- False

Q7. INSTRUCTIONS FOR EXERCISES 7 – 12: Specify what, if anything, is the main problem with the following generalizations from samples. There might be more than one problem, but indicate the main one.

This philosophy class is about logic, so most philosophy classes are probably about logic.

**The sample is too small.**- The sample is biased.
- The question is slanted.
- Nothing is wrong with this argument.

Q8. Most college students like to surf, because I asked a lot of students at several colleges along the California coast, and most of them like to surf.

- The sample is too small.
**The sample is biased.**- The question is slanted.
- Nothing is wrong with this argument.

Q9. A poll asked fifty thousand randomly chosen people throughout Asia whether they would want to eat foods that have been genetically modified in ways that increase company profits but also might poison them. Less that 10% replied “Yes, definitely.” Therefore, most people in Asia do not want to eat genetically modified foods.

- The sample is too small.
- The sample is biased.
**The question is slanted.**- Nothing is wrong with this argument.

Q10. K-Mart asked all of their customers throughout the country whether they prefer K-Mart to Walmart, and 90 percent said they did. Thus, 90 percent of all shoppers in the country prefer K-Mart.

- The sample is too small.
**The sample is biased.**- The question is slanted.
- Nothing is wrong with this argument.

Q11. Most Swedes are thieves, because my bicycle has been stolen twice, and both times it was a Swede who did it.

**The sample is too small.**- The sample is biased.
- The question is slanted.
- Nothing is wrong with this argument.

Q12. I have lots and lots of friends. All of them think that I would make a great comedian. So most people in my country would probably agree that I would make a great comedian.

- The sample is too small.
**The sample is biased.**- The question is slanted.
- Nothing is wrong with this argument.

#### Quiz 4: Applying Generalizations

Q1. The attribute class occurs in the conclusion when we apply a generalization to a case in an argument of the form: Almost all F are G, and a is F, so a is G.

**True**- False

Q2. The reference class occurs in the conclusion when we apply a generalization to a case in an argument of the form: Almost all F are G, and a is F, so a is G.

- True
**False**

Q3. An argument that applies a generalization to a case is never strong when the percentage in the premise is very low.

- True
**False**

Q4. An argument that applies a generalization to show that a case has a certain property is never strong when the percentage in the premise is 50%.

**True**- False

Q5. Arguments that apply a generalization to a case are intended to be valid.

- True
**False**

Q6. Arguments that apply a generalization to a case are defeasible.

**True**- False

Q7. An argument from the premise that 99% of F are G to the conclusion that this F (namely, a) is G is stronger than an argument to the same conclusion from the premise that 90% of F are G.

**True**- False

Q8. Arguments that apply a generalization to a case commit the fallacy of overlooking a conflicting reference class when another smaller reference class that was not mentioned in the argument has a very different (higher or lower) percentage of Gs that would support a conflicting conclusion.

**True**- False

Q9. INSTRUCTIONS FOR QUESTIONS 9-12: Specify what, if anything, is the main problem with the following applications of generalizations to cases. There might be more than one problem, but indicate the main one.

Almost all Prime Ministers of Great Britain have been men.;

Margaret Thatcher was Prime Minister of Great Britain.

So Margaret Thatcher is a man.

- The percentage is too low.
- The percentage is too high.
**The argument overlooks a conflicting reference class.**- Nothing is wrong with this argument.

Q10. The weather forecast says that there is only a 40% chance of rain, so it won’t rain, and we don’t need to bring an umbrella.

- The percentage is too low.
**The percentage is too high.**- The argument overlooks a conflicting reference class.
- Nothing is wrong with this argument.

Q11. Our heater works most of the time, so we can depend on it to keep us warm during the blizzard that is coming.

**The percentage is too low.**- The percentage is too high.
- The argument overlooks a conflicting reference class.
- Nothing is wrong with this argument.

Q12. Very few birds can swim, and this duck is a bird, so this duck cannot swim.

- The percentage is too low.
- The percentage is too high.
**The argument overlooks a conflicting reference class.**- Nothing is wrong with this argument.

#### Quiz 5: Inference to the Best Explanation

Q1. The purpose of an inference to the best explanation is to justify its conclusion.

**True**- False

Q2. Detectives use inference to the best explanation to solve murder mysteries.

**True**- False

Q3. Scientists use inference to the best explanation to draw conclusions from observations in their experiments.

**True**- False

Q4. Inferences to the best explanation are intended to be valid.

- True
**False**

Q5. Inferences to the best explanation are defeasible.

**True**- False

Q6. Inferences to the best explanation are deductive.

- True
**False**

Q7. Inferences to the best explanation include a premise about an observation that needs to be explained.

**True**- False

Q8. The conclusion of an inference to the best explanation is supposed to explain an observation in one of the premises.

**True**- False

Q9. One premise in an inference to the best explanation claims that one explanation is better than others.

**True**- False

Q10. If two competing explanations of the same event are equally good, then we can use an inference to the best explanation to justify belief in one of those explanations.

- True
**False**

#### Quiz 6: Which Explanation Is Best?

Q1. One explanation is better than another when it has more of the explanatory virtues.

**True**- False

Q2. Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, “Your explanation won’t explain anything other than this particular case.” Which explanatory virtue is this critic claiming that your explanation lacks?

- Falsifiability
- Conservativeness
**Power (or Breadth)**- Depth
- Modesty

Q3. Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, “Your explanation conflicts with everything we know about biology.” Which explanatory virtue is this critic claiming that your explanation lacks?;

- Falsifiability
**Conservativeness**- Power (or Breadth)
- Depth
- Modesty

Q4. Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, “You don’t have to claim so much in order to explain what happened.” Which explanatory virtue is this critic claiming that your explanation lacks?

- Falsifiability
- Conservativeness
- Power (or Breadth)
- Depth
**Modesty**

Q5. Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, “Your explanation just raises new questions that you also need to answer.” Which explanatory virtue is this critic claiming that your explanation lacks?

- Falsifiability
- Conservativeness
- Power (or Breadth)
**Depth**- Modesty

Q6. Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, “Your explanation would apply to whatever happened.” Which explanatory virtue is this critic claiming that your explanation lacks?

**Falsifiability**- Conservativeness
- Power (or Breadth)
- Depth
- Modesty

Q7. Indicate which explanatory virtue is the main one that is lacking from this explanation: I fished here all day, but I did not catch any fish, because there are no fish anywhere in this river.

- Falsifiability
- Conservativeness
- Power (or Breadth)
- Depth
**Modesty**

Q8. Indicate which explanatory virtue is the main one that is lacking from this explanation: My car won’t start today, because it is mad at me for driving it so much.

- Falsifiability
**Conservativeness**- Power (or Breadth)
- Depth
- Modesty

Q9. Indicate which explanatory virtue is the main one that is lacking from this explanation: Her flowers won’t grow because something is wrong with them.

- Falsifiability
- Conservativeness
- Power (or Breadth)
**Depth**- Modesty

Q10. Indicate which explanatory virtue is lacking from this explanation: I lost the race because I just did not happen to run well today.

- Falsifiability
- Conservativeness
**Power (or Breadth)**- Depth
- Modesty

#### Quiz 7: A Student Example: Inference to the Best Explanation

Q1. In the situation described in the student video in the lecture, which virtue of explanations would be lacking from the hypothesis that Timmy the Cat knocked the cookies off the counter because he was trying to eat one of them?

- Falsifiability
- Power or Breadth
**Modesty**- Conservativeness

Q2. In the situation described in the student video in the lecture, which virtue of explanations would be lacking from the hypothesis that ghosts knocked the cookies off the counter?

- Falsifiability
- Power or Breadth
- Modesty
**Conservativeness**

Q3. In the situation described in the student video in the lecture, what is wrong with the hypothesis that a burglar knocked over the cookies after breaking in to steal something?

- It is not falsifiable.
- It cannot explain the cat hair on the counter.
- There is no evidence of anyone breaking in.
- Nothing was stolen.
**More than one of the above**

#### Quiz 8: Arguments from Analogy

Q1. Arguments from analogy are used in art but not in science.

- True
**False**

Q2. Every similarity between Earth and Mars provides some reason to believe that, since there is life on Earth, there is also life on Mars.

- True
**False**

Q3. Arguments from analogy are usually intended to be valid.

- True
**False**

Q4. Arguments from analogy are defeasible.

**True**- False

Q5. Arguments from analogy are inductive.

**True**- False

Q6. Arguments from analogy are stronger when the conclusion is weaker.

**True**- False

Q7. Arguments from analogy are stronger when they cite more relevant analogies between the objects.

**True**- False

Q8. Some arguments from analogy can be reconstructed as inferences to the best explanation.

**True**- False

Q9. When you give an argument from analogy, you need to specify which similarity is the one that is important for the conclusion.

- True
**False**

Q10. Consider this argument from analogy to answer questions 10-12:

I have seen many movies about James Bond (007). I almost always enjoyed them. A new James Bond movie just came out. I have not seen it yet, but I know that it resembles previous James Bond movies in many respects, such as action, style, and ingenious devices. So I will probably enjoy the new James Bond movie as well, if I watch it.

Would this argument from analogy become stronger, weaker, or neither if we added a premise that the new James Bond movie has a new actor playing James Bond?

- Stronger
**Weaker**- Neither stronger nor weaker

Q11. Would the argument from analogy in Question 10 become stronger, weaker, or neither if we added a premise that the previous James Bond movies had five or fewer words in their titles, but the new James Bond movie has eight words in its title?

- Stronger
- Weaker
**Neither stronger nor weaker**

Q12. Would the argument from analogy in Question 10 become stronger, weaker, or neither if we added a premise that the previous James Bond movies and new James Bond movie are also similar in more respects that I usually like, such as exotic settings, beautiful actors, intrigue, and so on?

**Stronger**- Weaker
- Neither stronger nor weaker

Q13. Consider this argument from analogy to answer questions 13-15:

A new drug cures a serious disease in rats. Rats are similar to humans in many respects. Therefore, this new drug will probably cure the same disease in humans.

Would this argument from analogy become stronger, weaker, or neither if we added a premise that the disease affects the liver, and livers in rats and in humans are very similar in structure and function?

**Stronger**- Weaker
- Neither stronger nor weaker

Q14. Would the argument from analogy in Question 13 become stronger, weaker, or neither if we added a premise that the drug does not cure this disease in monkeys or pigs?

- Stronger
**Weaker**- Neither stronger nor weaker

Q15. Would the argument from analogy in Question 13 become stronger, weaker, or neither if we added that most of the cured rats were conceived on weekdays (because that is when lab technicians were around to enable conception) whereas most humans were conceived on weekends (when they had more free time)?

- Stronger
- Weaker
**Neither stronger nor weaker**

### Week 2: Think Again III: How to Reason Inductively Coursera Quiz Answers

#### Quiz 1:Causal Reasoning

Q1. All sufficient conditions are causes.

- True
**False**

Q2. When F is sufficient for G, there are no possible cases of F without G.

- True
**False**

Q3. When F is necessary for G, there are no cases of G without F in normal circumstances.

**True**- False

Q4. Being a car is a sufficient condition for being a vehicle.

**True**- False

Q5. Being a car is a necessary condition for being a vehicle.

- True
**False**

Q6. Being a vehicle is a sufficient condition for being a car.

- True
**False**

Q7. Being a vehicle is a necessary condition for being a car.

**True**- False

Q8. Being an integer is a sufficient condition for being an even number.

- True
**False**

Q9. Being an integer is a necessary condition for being an even number.

**True**- False

Q10. Being an integer is a sufficient condition for being either an even number or an odd number.

**True**- False

Q11. Cutting off Joe’s head is a sufficient condition for killing him.

**True**- False

Q12. Cutting off Joe’s head is a necessary condition for killing him.

- True
**False**

#### Quiz 2: Negative Sufficient Condition Tests

Q1. X is not a sufficient condition of Y if there is any case in the current data where X is present and Y is absent.

**True**- False

Q2. X is a sufficient condition of Y if there is not any case in the current data where X is present and Y is absent.

- True
**False**

Q3. Even if the current data include one case of X without Y, future cases still might show that X is sufficient for Y.

- True
**False**

Q4. INSTRUCTIONS FOR QUESTIONS 4 – 10:

Imagine that some diners died directly after dinner. (Alliteration!) We know that something they ate caused the deaths. This is all they ate:

Alice had tomato soup, eggplant, iced tea, and cake — and Alice died.

Branden ate pea soup, chicken, water, and ice cream — and Branden did not die.

Carol had tomato soup, chicken, water, and cake — and Carol died.

Davida ate pea soup, eggplant, iced tea, and ice cream — and Davida did not die.

Ernie had tomato soup, fish, iced tea, and pie — and Ernie did not die.

Based on this data, which diner shows that eggplant is not sufficient for death?

- Alice
- Branden
- Carol
**Davida**- Ernie
- None of these diners

Q5. Based on the data in Question 4, which diner shows that tomato soup is not sufficient for death?

- Alice
- Branden
- Carol
- Davida
**Ernie**- None of these diners

Q6. Based on the data in Question 4, which diner shows that cake is not sufficient for death?

- Alice
- Branden
- Carol
- Davida
- Ernie
**None of these diners**

Q7. Based on the data in Question 4, which diner shows that water is not sufficient for death?

- Alice
**Branden**- Carol
- Davida
- Ernie
- None of these diners

Q8. Based on the data in Question 4, which of the following does the case of Branden rule out as sufficient for death?

- Pea soup
- Chicken
- Water
- Ice cream
**All four of the things Branden had**- Nothing

Q9. Based on the data in Question 4, which of the following does the case of Carol rule out as sufficient for death?

- Pea soup
- Chicken
- Water
- Ice cream
- All four of the things Carol had
**Nothing**

Q10. Based on the data in Question 4, which individual diner shows that something is sufficient for death?

- Alice
- Branden
- Carol
- Davida
- Ernie
**None of these diners**

Q11. You can construct your own examples for practicing simply by changing the outcomes (died vs. did not die) and the foods (soup, dessert, etc.) for the diners in the data in Question 4.

**True**- False

#### Quiz 3: Positive Sufficient Condition Tests

Q1. A set of data can sometimes give us good reason to believe that X is a sufficient condition of Y even if that set does not include any cases where Y is absent.

- True
**False**

Q2. We have good reason to believe that X is a sufficient condition of Y if (i) we have not found any case where X is present and Y is absent, (b) we have tested a wide variety of cases, including cases where X is present and cases where Y is absent, and (c) if there is any other feature that is never present where Y is absent, then we have tested cases where that other feature is absent but X is present as well as cases where that other feature is present but X is absent.

- True
**False**

Q3. The positive sufficient condition test is inductive.

**True**- False

#### Quiz 4: Negative Necessary Condition Tests

Q1. X is not a necessary condition of Y if there is any case in the current data where X is absent and Y is present.

**True**- False

Q2. X is a necessary condition of Y if there is not any case in the current data where X is absent and Y is present.

- True
**False**

Q3. Even if the current data include one case of Y without X, future cases still might show that X is necessary for Y.

- True
**False**

Q4. INSTRUCTIONS FOR QUESTIONS 4 – 9:

Imagine that some diners died directly after dinner. (Alliteration!) We know that something they ate caused the deaths. This is all they ate:

Alice had tomato soup, eggplant, iced tea, and cake — and Alice died.

Branden ate pea soup, chicken, water, and ice cream — and Branden did not die.

Carol had tomato soup, chicken, water, and cake — and Carol died.

Davida ate pea soup, eggplant, iced tea, and ice cream — and Davida did not die.

Ernie had tomato soup, fish, iced tea, and pie — and Ernie did not die.

(NOTICE: This is the same data as in Question 4 of the Exercises for Lecture 7-2.)

Based on this data, which diner shows that iced tea is not necessary for death?

- Alice
- Branden
**Carol**- Davida
- Ernie
- None of these diners

Q5. Based on the data in Question 4, which diner shows that chicken is not necessary for death?

**Alice**- Branden
- Carol
- Davida
- Ernie
- None of these diners

Q6. Based on the data in Question 4, which diner shows that tomato soup is not necessary for death?

- Alice
- Branden
- Carol
- Davida
- Ernie
**None of these diners**

Q7. Based on the data in Question 4, which of the following does the case of Carol rule out as necessary for death?

- Pea soup
- Eggplant
- Fish
- Iced tea
- Ice cream
- Pie
**All of the above**- Nothing

Q8. Based on the data in Question 4, which of the following does the case of Ernie rule out as necessary for death?

- Pea soup
- Eggplant
- Chicken
- Water
- Ice cream
- Cake
- All of the above
**Nothing**

Q9. Based on the data in Question 4, which individual diner shows that something is necessary for death?

- Alice
- Branden
- Carol
- Davida
- Ernie
**None of these diners**

Q10. There is no simple way to construct your own examples in order to practice by changing the outcomes (died vs. did not die) and the foods (soup, dessert, etc.) for the diners in the data in Question 4.

- True
- False

#### Quiz 5: Positive Necessary Condition Tests

Q1. We have good reason to believe that X is a necessary condition of Y if (i) we have not found any case where X is absent and Y is present, (b) we have tested a wide variety of cases, including cases where X is absent and cases where Y is present, and (c) if there are any other features that are never absent where Y is present, then we have tested cases where those other features are present but X is absent as well as cases where those other features are absent but X is present.

- True
**False**

Q2. The positive necessary condition test is deductive.

- True
**False**;

#### Quiz 6: Complex Conditions

Q1. A conjunctive condition—W and X—is not sufficient for Y if there is any case where W and X are both present but Y is absent.

**True**- False

Q2. A conjunctive condition—W and X—is not sufficient for Y if there is any case where X is present but Y is absent.

- True
**False**

Q3. A disjunctive condition—W or X—is not sufficient for Y if there are any cases where X is present but Y is absent.

**True**- False

Q4. INSTRUCTIONS FOR QUESTIONS 4 – 9:

Imagine that you buy a new computer system with independent components including a new desktop computer (with a CPU and a graphics card), new software, and a new monitor. You want to play games on the new system, but it runs games very slowly. You assume that the keyboard and mouse are not creating the problem; so, to figure out what is making the system run so slowly, you experiment with combinations of your old equipment with the new equipment. Here are your experiments and results:

Experiment 1: New computer, new software, and new monitor — and it runs slowly.

Experiment 2: New computer, new software, and old monitor — and it runs fast.

Experiment 3: New computer, old software, and new monitor — and it runs fast.

Experiment 4: New computer, old software, and old monitor — and it runs fast.

Experiment 5: Old computer, new software, and new monitor — and it runs slowly.

Experiment 6: Old computer, new software, and old monitor — and it runs fast.

Experiment 7: Old computer, old software, and new monitor — and it runs slowly.

Experiment 8: Old computer, old software, and old monitor — and it runs fast.

Based on this data, which experiment shows that the new monitor is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
**Experiment 3**- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of these experiments;

Q5. Based on the data in Question 4, which experiment shows that the conjunction of the new computer and the new monitor is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
**Experiment 3**- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of these experiments

Q6. Based on the data in Question 4, which experiment shows that the conjunction of the new computer and the new software is not sufficient for the system to run slowly?

- Experiment 1
**Experiment 2**- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of these experiments

Q7. Based on the data in Question 4, which experiment shows that the conjunction of the new software and the new monitor is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
**None of these experimients**

Q8. data in Question 4, which Experiment shows that the conjunction of the old computer and the old software is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
**Experiment 8**- None of these experiments

Q9. Based on the data in Question 4, which Experiment shows that the conjunction of the old computer and the new monitor is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
**None of these experiments**;

#### Quiz 7: Correlation Versus Causation

Q1. X and Y are positively correlated if the degree of X increases as the degree of Y decreases and the degree of X decreases as the degree of Y increases.

- True
**False**

Q2. If X and Y are positively correlated, then they are positively correlated in all circumstances.

- True
**False**

Q3. When A and B are correlated, which of the following is possible?

- A causes B.
- B causes A.
- A third thing causes both A and B.
- There is no causal relation between A and B.
**Each of the other four answers is possible.**

Q4. Assume that the quality of a musician’s performance is positively correlated with how much practicing the musician did for the performance. Which of the following is most likely?

**The practice causes the quality of the performance.**- The quality of the performance causes the practice.
- A third thing causes both the practice and the quality of the performance.
- There is no causal relation between the practice and the quality of the performance.

Q5. The amount of light next to an active fire is positively correlated with the amount of heat in that location. Which of the following is most likely?

- The light causes the heat.
- The heat causes the light.
**A third thing causes both the light and the heat.**- There is no causal relation between the light and the heat.

Q6. Assume that A and B are correlated. If A changes when you manipulate B, but B does not change when you manipulate A, then which of the following is most likely? Assume normal circumstances and no interfering factors.

- A causes B.
**B causes A.**- A third thing causes both A and B.
- There is no causal relation between A and B.

Q7. Assume that A and B are correlated. If B changes when you manipulate A, but A does not change when you manipulate B, then which of the following is most likely? Assume normal circumstances and no interfering factors.

**A causes B.**- B causes A.
- A third thing causes both A and B.
- There is no causal relation between A and B.;

#### Quiz 8: Causal Fallacies

Q1. An argument commits the fallacy called “post hoc, ergo propter hoc” when it concludes that A causes B from the premise that A occurred before B.

**True**- False

Q2. An argument confuses cause with effect when it uses a correlation to argue that A causes B when actually B causes A.

**True**- False

Q3. The fallacy of confusing cause and effect occurs only in science.

- True
**False**

Q4. Consider this argument: After I argued that Johnson is the best candidate for President, she said that she supports Johnson, too. So she must have been convinced by my arguments.

Which of the following fallacies does it commit?

**Post Hoc Ergo Propter Hoc**- Confusing Cause with Effect
- Neither of the Above;

### Week 3: Think Again III: How to Reason Inductively Coursera Quiz Answers

#### Quiz 1: Why Probability Matters

Q1. If a fair coin comes up heads five times in a row, then the probability that it will come up heads on the next flip is:

- One half (0.5)
**Less than one half**- More than one half (> 0.5)

Q2. If a fair dealer deals you five cards out of a shuffled fair standard deck of cards, then which of the following hands is most likely?

- Ace of Hearts, King of Hearts, Queen of Hearts, Jack of Hearts, and Ten of Hearts
- Ace of Hearts, King of Hearts, Queen of Hearts, Jack of Hearts, and Five of Clubs
- Ace of Hearts, Jack of Hearts, Nine of Diamonds, Seven of Clubs, and Five of Clubs
**All of these hands are equally likely.**

Q3. As described in the lecture, Linda is thirty-one years old, single, outspoken, and very bright. As a student, she majored in philosophy, was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. Which of the following is most likely?

**Linda is a bank teller.**- Linda is a bank teller who is active in the feminist movement.
- These possibilities are equally likely.

Q4. Imagine that you are playing the old television game show “Let’s Make a Deal” hosted by Monte Hall and described in the lecture. You face three closed doors. Behind one of the doors is a car. Behind each of the other two doors is a goat. You pick door A, so you will get to keep what is behind door A if you stick with it. Then, as always, Monte Hall opens one of the remaining two doors, reveals a goat behind that other door, and offers you the opportunity to switch doors, if you want. Suppose that this time Monte Hall opens door C and offers you the opportunity to switch to door B. If you switch doors, then you will get what is behind door B instead of what is behind door A. If you do not switch doors, then you will get what is behind door A. Should you switch doors?

**You should switch doors.**- You should not switch doors.
- It does not matter whether or not you switch doors.;

#### Quiz 2: What Is Probability?

Q1. If the probability of an event is 0.73, then its probability can also be expressed as

- 73% chance
- 73 out of 100
- 7.3 out of 10
**All of the above**- None of the above

Q2. It is possible for some events to have a probability of

- 1.5
- –1.5
- Both of the above are possible for different events.
**None of the above.**

Q3. If the probability of an event is 1.0, then

**It is certain that it will happen.**- It is certain that it will not happen.
- It might or might not happen.

Q4. When someone assumes that six-sided dice are equally likely to fall on any of the sides—1, 2, 3, 4, 5, or 6—then that person is calculating

**A priori probability**- Statistical probability
- Subjective probability

Q5. When a coin is bent, the most accurate way to determine the probability that it will land heads up when it is flipped is to use:

- A priori probability
**Statistical probability**- Subjective probability;

Q6. A coin flip is fair when the coin is equally likely to land with either side—heads or tails—up, and the coin will always land on either heads or tails but not on its edge. If we assume that a coin flip is fair, then the probability that the coin will land heads up is:

- 0
- 0.25
**0.5**- 0.75
- 1

Q7. A roll of a six-sided die is fair when the die is equally likely to land with any of its sides—1, 2, 3, 4, 5, or 6—up, and the die will always land with one of those sides up. If we assume that a roll of a six-sided die is fair, then the probability that the die will land with 4 up is:

- 0
**1/6**- 3/6
- 4/6
- 1

Q8. A roll of a ten-sided die is fair when the die is equally likely to land with any of its sides—1, 2, 3, 4, 5, 6, 7, 8, 9, or 10—up, and the die will always land with one of those sides up. If we assume that a roll of a ten-sided die is fair, then the probability that the die will land with 4 up is:

- 0
**1/10**- 3/10
- 4/10
- 1

Q9. A roll of two dice is X when the sum of the numbers on the two sides that land up is X. If we assume that the roll is fair, what is the probability that one roll of two six-sided dice will be 4 (that is, will land with a total of 4 up)?

- 0
**3/36**- 3/6
- 4/6
- A1;

#### Quiz 3: Negation

Q1. If the probability that a flipped coin will land heads up is 0.5, what is the probability that it will NOT land heads up?

- 0
- 0.25
**0.5**- 0.75
- 1.0

Q2. Imagine that you bend the coin in Question 1 so that the probability that it will land heads up when flipped is 0.25. Now what is the probability that it will NOT land heads up?

- 0
- 0.25
- 0.5
**0.75**- 1.0

Q3. As shown in Lecture 8-02, the probability of rolling a seven on two fair six-sided dice is 6/36. What is the probability of NOT rolling a seven on two fair six-sided dice?

- 0
- 6/36
- 18/36
**30/36**- 1.0

Q4. The probability of picking an ace at random out of a fair standard deck of cards is 1/13. What is the probability of NOT picking an ace out of this deck?

- 0
- 1/13
- 9/13
**12/13**- 1.0

Q5. The probability of picking a spade at random out of a fair standard deck of cards is 1/4. What is the probability of NOT picking a spade at random out of this deck?

- 0
- 1/4
- 2/4
**3/4**- 1.0

Q6. Imagine that you own one ticket to a lottery where the chances of this ticket winning are one in 1,000,000. What is the probability of this ticket NOT winning?

- 0
- 1/1,000,000
- 9/10
**999,999/1,000,000**- 1.0

Q7. If the probability of an event is 0.1, what is the probability that either that event will occur or that event will not occur?

- 0
- 0.1
- 0.5
- 0.9
**1.0**;

#### Quiz 4: Conjunction

Q1. Two events are independent (in the sense used in the rules for probability) if and only if

- They cannot possibly both occur together.
**Whether or not one of the events occurs does not affect the probability that the other event will occur.**- Neither of the events depends on anything else in order to occur.

Q2. If two events are independent, then the probability of both events occurring is

- The sum of the probability of the first event plus the probability of the second event.
- The difference of the probability of the first event minus the probability of the second event.
**The product of the probability of the first event times the probability of the second event.**

Q3. If two events are NOT independent, then the probability of both events occurring is

- The product of the probability of the first event times the probability of the second event.
- The product of the probability of the first event times the probability of both the first event and the second event.
**The product of the probability of the first event times the conditional probability of the second event given the first event.**- The product of the probability of the first event times the conditional probability of the first event given the second event.

Q4. The conditional probability of one event (X) given another event (Y) is:

**The percentage of cases where X occurs out of the cases where Y occurs.**- The percentage of cases where Y occurs out of the cases where X occurs.
- The probability that both X and Y occur.

Q5. Assuming that all coin flips here are fair, the flip of one coin and the flip of another coin are:

**Independent**- Not independent
- Sometimes independent and sometimes not independent

Q6. Assuming that all coin flips here are fair, what is the probability of getting tails on two flips in a row of the same coin?

- 0
**0.25**- 0.5
- 0.75
- 1

Q7. Assuming that all dice rolls here are fair, what is the probability of getting three on both dice (that is, 3 on one and also 3 on the other for a total of 6) when you roll two 6-sided dice at the same time?

- 0
**1/36**- 1/6
- 2/6
- 1

Q8. Assuming that all card picks here are fair, what is the probability of getting a spade on two picks out of a standard deck when you replace the card that you picked first and shuffle the deck before you pick the second card?

**1/16**- 2/4
- 1
- 0
- 1/4

Q9. Assuming that all card picks here are fair, when you pick two cards out of a deck, and you do not replace the card that you picked first before you pick the second card, then the probabilities of getting a Jack on both picks are:

- Independent
**Not independent**- Sometimes independent and sometimes not independent

Q10. Assuming that all card picks here are fair, imagine that you pick a King of Hearts out of a standard deck, and you do not put that card back in the deck, then what is the probability that you will pick a Queen on the next pick out of the remaining deck?

- 4/52
- 4/52 x 4/52
**4/51**- 4/52 x 4/51;

Q11. Assuming that all card picks here are fair, imagine that you pick a Queen of Hearts out of a standard deck, and you do not put that card back in the deck, then what is the probability that you will pick a Queen on the next pick out of the remaining deck?

- 4/52
- 4/51
- 3/52
**3/51**

Q12. Assuming that all card picks here are fair, what is the probability that you will pick a King and then a Queen out of a standard deck when you do not put the card that you picked first back in the deck?

- 4/52
- 4/52 x 4/52
- 4/51
**4/52 x 4/51**

Q13. Assuming that all card picks here are fair, what is the probability that you will pick two Queens in two draws out of a standard deck when you do not put the card that you picked first back in the deck:

- 4/52 x 4/52
- 4/52 x 4/51
- 4/52 x 3/52
**4/52 x 3/51**

Q14. Assuming that all card picks here are fair, what is the probability that you will pick a Spade and then a Heart out of a standard deck when you do not put the card that you picked first back in the deck?

- 4/52 x 4/51
- 4/52 x 4/52
**13/52 x 13/51**- 13/52 x 13/52

Q15. You can construct your own examples for practicing simply by asking about other outcomes on flips of coins, rolls of dice, and picks of cards.

- Quiz
**True** - False

#### Quiz 5: Disjunction

Q1. Two events are mutually exclusive if and only if

**They cannot possibly both occur together.**- Whether or not one of the events occurs does not affect the probability that the other event will occur.
- Neither of the events excludes anything else.

Q2. If two events are mutually exclusive, then the probability of either one event or the other event occurring is

**The sum of the probability of the first event plus the probability of the second event.**- The difference of the probability of the first event minus the probability of the second event.
- The product of the probability of the first event times the probability of the second event.

Q3. If two events are NOT mutually exclusive, then the probability of either one event or the other event occurring is

- The sum of the probability of the first event plus the probability of the second event.
- The sum of the probability of the first event plus the probability of both the first event and the second event.
**The sum of the probability of the first event plus the probability of the second event minus the probability of both the first event and the second event occurring together.**- The sum of the probability of the first event plus the conditional probability of the first event given the second event.

Q4. On one fair flip of a single coin, getting heads and getting tails are:

**Mutually exclusive**- Not mutually exclusive
- Sometimes mutually exclusive and sometimes not mutually exclusive

Q5. On one fair flip of a single coin, what is the probability of getting either heads or tails?

- 0
- 0.25
- 0.5
- 0.75
**1**;

Q6. Assuming that all dice rolls here are fair, what is the probability of getting either two or three when you roll one 6-sided die?

- 0
- 1/6
**2/6**- 3/6
- 1

Q7. Assuming that all dice rolls here are fair, what is the probability of getting three on either one die or the other die when you roll two 6-sided dice at the same time?

- 1/36
- 1/6
- 2/6
**2/6 – 1/36**- 2/6 + 1/36

Q8. Assuming that all card picks here are fair, what is the probability of getting either a spade or a club when you pick one card out of a standard deck?

- 0
- 1/4
**2/4**- 3/4
- 1

Q9. Assuming that all card picks here are fair, what is the probability of picking a spade on either the first pick or the second pick when you pick two cards out of a standard deck (and when you put the first card back and shuffle the cards before the second pick)?

- 1/16
- 1/4
- 2/4
**2/4 – 1/16**- 2/4 + 1/16;

Q10. Assuming that all card picks here are fair, what is the probability of getting either a six or a seven when you pick one card out of a standard deck?

- 0
- 1/13
**2/13**- 3/13
- 1

Q11. Assuming that all card picks here are fair, what is the probability of picking a seven on either the first pick or the second pick when you pick two cards out of a standard deck (and when you put the first card back and shuffle the cards before the second pick)?

- 1/13 x 1/13
- 1/13
- 2/13
**2/13 – (1/13 x 1/13)**- 2/13 + (1/13 x 1/13)

Q12. Which of the following is accurate?

- Order of events matters in combinations but not in permutations.
**Order of events matters in permutations but not in combinations.**- Order of events matters in both combinations and permutations.
- Order of events matters in neither combinations nor permutations.

Q13. Assuming that all card picks here are fair, what is the probability of picking an eight and a nine in any order when you pick two cards out of a standard deck (when you put the first card back and shuffle the cards before the second pick)?

- 1/13 x 1/13
- 1/13 + 1/13
- 2/13 + 2/13
**(1/13 x 1/13) + (1/13 x 1/13)**- (1/13 + 1/13) x (1/13 + 1/13)

Q14. Imagine that there are two little lotteries in your town. Each lottery sells exactly 100 tickets each and has only one winning ticket. You pick one of these lotteries and buy two tickets to the same lottery. What is the probability that you will have one winning ticket (that is, the probability that either your first ticket or your second ticket will win)?

- 1/100
- 1/100 x 1/100
**1/100 + 1/100**- 1/100 + 1/100 – (1/100 x 1/100)
- (1/100 x 1/100) – (1/100 + 1/100)

Q15. As in Question 14, imagine that there are two little lotteries in your town. Each lottery sells exactly 100 tickets each and has only one winning ticket. You buy one ticket to each of these two lotteries. What is the probability that you will have at least one winning ticket (that is, the probability that either your first ticket, your second ticket, or both will win)?

- 1/100
- 1/100 x 1/100
- 1/100 + 1/100
**1/100 + 1/100 – (1/100 x 1/100)**- (1/100 x 1/100) – (1/100 + 1/100)

Q16. You can construct your own examples for practicing simply by asking about other outcomes on flips of coins, rolls of dice, and picks of cards.

**True**- False;

#### Quiz 6: Series

Q1. What is the probability of getting heads at least once in a series of three fair flips of a coin?

- 0.125
- 0.25
- 0.5
- 0.75
**0.875**

Q2. What is the probability of rolling seven at least once in a series of three fair rolls of two dice in each roll?

- 1/6
- 1/3
- 5/6
**91/216**- 125/216

Q3. What is the probability of drawing at least one spade in a series of four consecutive fair draws from a standard deck of cards, when the card drawn is returned to the deck and the deck is shuffled between each draw?

- 1/16
- 1/4
- 3/4
- 81/256
**175/256**

Q4. You can construct your own examples for practicing simply by asking about other series of flips of coins, rolls of dice, and picks of cards.

**True**- False;

#### Quiz 7: Bayes Theorem (Optional)

Q1. A FALSE POSITIVE (or a false alarm) is

- A case where the condition is present and the test comes out positive.
- A case where the condition is present and the test comes out negative.
- A case where the condition is absent and the test comes out positive.
- A case where the condition is absent and the test comes out negative.

Q2. A FALSE NEGATIVE (or a miss) is

- A case where the condition is present and the test comes out positive.
**A case where the condition is present and the test comes out negative.**- A case where the condition is absent and the test comes out positive.
- A case where the condition is absent and the test comes out negative.

Q3. The BASE RATE or PREVALENCE of a condition in a population is

- The number of people in the population.
**The percentage of the population with the condition.**- The probability of a positive test result, given that the person tested does have the condition.
- The probability of a negative test result, given that the person tested does not have the condition.

Q4. The SENSITIVITY of a test for a condition is

- The probability of a positive test result.
- The probability of a negative test result.
- The probability of a positive test result, given that the person tested does have the condition.
- The probability of a negative test result, given that the person tested does not have the condition.

Q5. The SPECIFICITY of a test for a condition is

- The probability of a positive test result.
- The probability of a negative test result.
- The probability of a positive test result, given that the person tested does have the condition.
- The probability of a negative test result, given that the person tested does not have the condition.;

Q6. INSTRUCTIONS FOR QUESTIONS 6–14:

Assume that

(A) The base rate or prevalence of colon cancer in a population is 0.1% or 0.001.

(B) The sensitivity of a certain test for colon cancer is 90%. (Sensitivity is the probability of a positive test result, given that the person tested does have colon cancer.)

(C) The specificity of that same test for colon cancer is 97%. (Specificity is the probability of a negative test result, given that the person tested does not have colon cancer.)

Use these ASSUMPTIONS to fill the boxes in this TABLE:

What number belongs in Box 7?

- 10
- 90
- 100
- 1000
- 99,900

Q7. What number belongs in Box 8?

- 10
- 90
- 100
- 1000
- 99,900

Q8. What number belongs in Box 1?

- 10
**90**- 100
- 1000
- 99,900

Q9. What number belongs in Box 4?

**10**- 90
- 100
- 1000
- 99,900

Q10. What number belongs in Box 5?

- 2997
- 3087
- 96,903
- 99,000
- 99,900

Q11. What number belongs in Box 2?

**2997**- 3087
- 96,903
- 99,000
- 99,900

Q12. What number belongs in Box 3?

- 90
- 2997
- 3087
- 96,903
- 96,913

Q13. What number belongs in Box 6?

- 10
- 2997
- 3087
- 96,903
- 96,913

Q14. In the case described in Question 6, what is the probability that a patient has colon cancer given that the patient tests positive for colon cancer with this test?

- 10/3087
**90/3087**- 100/3087
- 2997/3087
- 90/100,000;

Q15. Suppose that the situation is exactly like the case in Question 6 except that the base rate is higher:

- (A) The base rate or prevalence of colon cancer in a population is 10% or 0.1.
- (B) The sensitivity of a certain test for colon cancer is 90%. (Sensitivity is the probability of a positive test result, given that the person tested does have colon cancer.)
- (C) The specificity of that same test for colon cancer is 97%. (Specificity is the probability of a negative test result, given that the person tested does not have colon cancer.)

For this population and test, what is the probability that a patient has colon cancer given that the patient tests positive for colon cancer with this test?

- 27/90
- 27/117
- 90/117
- 10/883
- 873/883

Q16. Suppose that the situation is exactly like the case in Question 6 except that the sensitivity is higher:

- (A) The base rate or prevalence of colon cancer in a population is 0.1% or 0.001.
- (B) The sensitivity of a certain test for colon cancer is 99%. (Sensitivity is the probability of a positive test result, given that the person tested does have colon cancer.)
- (C) The specificity of that same test for colon cancer is 97%. (Specificity is the probability of a negative test result, given that the person tested does not have colon cancer.)

For this population and test, what is the probability that a patient has colon cancer given that the patient tests positive for colon cancer with this test?

- 1/99
- 99/2997
- 99/3096
- 2997/3096
- 96,903/96,904

Q17. Suppose that the situation is exactly like the case in Question 6 except that the specificity is higher:

- (A) The base rate or prevalence of colon cancer in a population is 0.1% or 0.001.
- (B) The sensitivity of a certain test for colon cancer is 90%. (Sensitivity is the probability of a positive test result, given that the person tested does have colon cancer.)
- (C) The specificity of that same test for colon cancer is 99%. (Specificity is the probability of a negative test result, given that the person tested does not have colon cancer.)

For this population and test, what is the probability that a patient has colon cancer given that the patient tests positive for colon cancer with this test?

- 90/999
**90/1089**- 999/1089
- 10/98,911
- 98,901/98,911

Q18. Suppose that a patient tests positive for colon cancer in the circumstances of Question 17, so there is an 8% chance that this patient has colon cancer. This information puts the patient in a new population—patients who have tested positive for colon cancer—with a higher base rate (8%) of colon cancer. Now suppose that the doctor orders a second test that is independent of the first test (because it looks for separate indications of colon cancer). This second test has the same specificity and sensitivity as the first test, so this new situation is:

(A) The base rate or prevalence of colon cancer in a population is 8% or 0.08.

(B) The sensitivity of the second test for colon cancer is 90%. (Sensitivity is the probability of a positive test result, given that the person tested does have colon cancer.)

(C) The specificity of the second test for colon cancer is 99%. (Specificity is the probability of a negative test result, given that the person tested does not have colon cancer.)

- 920/7200
- 920/8120
- 7200/8120
- 800/91,880
- 91,080/91,880

Q19. Chris tested positive for cocaine once in a random screening test. This test has a sensitivity and specificity of 90%, and 10 percent the students in Chris’s school use cocaine. What is the probability that Chris really did use cocaine?

**90/180**- 90/90
- 10/820
- 10/810
- 810/820

Q20. Late last night a car ran into your neighbor and drove away. In your town, there are 500 cars, and 2% of them are Porsches. The only eyewitness to the incident says that the car that hit your neighbor was a Porsche. Tested under similar conditions, the eyewitness mistakenly classifies cars of other makes as Porsches 10% of the time, and correctly classifies Porsches as Porsches 80% of the time. What are the chances that the car that hit your neighbor really was a Porsche?

- 8/49
**8/57**- 49/57
- 2/443
- 441/443

Q21. You can construct your own examples for practicing simply by asking about other cases with different base rates, sensitivities, and specificities.

**True**- False

#### Quiz 8: Expected Financial Value

Q1. The expected financial value of a bet is:

- The net gain of winning minus the net loss of losing
- The probability of winning minus the probability of losing
**The probability of winning times the net gain of winning minus the probability of losing times the net loss of losing**- The probability of winning times the net loss of losing minus the probability of losing times the net gain of winning

Q2. INSTRUCTIONS FOR QUESTIONS 2 – 8: In the following games, you lay down $1 to bet that you will pick a certain card in a fair draw from a standard deck. If you lose, then you lose your $1. If you win, then you collect the gross amount indicated, so your net gain is $1 less.

What is the expected financial value of a bet where you will win $26 if you draw a seven of spades?

- –$1
**–$0.50**- $0
- $25/52
- $0.50

Q3. What is the expected financial value of a bet where you will win $26 if you draw either a seven of spades or a seven of clubs?

- –$0.50
**$0**- $25/52
- $0.50
- $1

Q4. What is the expected financial value of a bet where you will win $26 if you draw a seven of any suit?

- –$0.50
- $0
- $25/52
- $0.50
**$1**

Q5. What is the expected financial value of a bet where you will win $4 if you draw either a Jack, a Queen, or a King?

- –$4/52
- $0
- $8/52
- $36/52
**$48/52**;

Q6. What is the expected financial value of a bet where you will win $2 if you do NOT draw either a Jack, a Queen, or a King?

**–$4/52**- $0
- $28/52
- $40/52
- $68/52

Q7. What is the expected financial value of a bet where you will win $2652 if you draw a seven of spades and then a seven of clubs on two consecutive draws (without returning the first card to the deck)?

- –$52/2704
- –$52/2652
**$0**- $1/2652
- $52/2704

Q8. What is the expected financial value of a bet where you will win $2652 if you draw a seven of spades and then a seven of clubs on two consecutive draws (where you replace the card and shuffle the deck between draws)?

**–$52/2704**- –$52/2652
- $0
- $1/2652
- $52/2704

Q9. You can construct your own examples for practicing simply by asking about other bets.

**True**- False;

#### Quiz 9: Expected Overall Value

Q1. Imagine that you are going to the drugstore to buy medicine for a friend. Your friend will die if you do not get the medicine on this trip to the drugstore, and nobody else will loan you money for the medicine. You have only $10 with you, and this is exactly what the medicine costs. Outside the drugstore is a young man playing three-card monte, a simple game in which the dealer shows you three cards, turns them over, shifts them briefly from hand to hand, and then lays them out, facedown, on the top of a box. You are supposed to identify a particular card; and, if you do, you are paid even money. You yourself are a magician and know the sleight-of-hand trick that fools most people, and you are sure that you can guess the card correctly nine times out of ten. In this situation, what is the expected financial value of a bet of $10?

- $0
**$8**- $9
- $10
- $20

Q2. Should you play the game in the circumstances in Question 1?

- Yes, you should play the game.
- No, you should not play the game .
- It is reasonable either to play or not to play to game.

Q3. In the game of ignorance, you draw one card from a deck. You do not know how many cards or which kinds of cards are in the deck. It might be a standard deck or it might contain only diamonds or only aces of spades or any other combination of cards. It costs nothing to play. If you bet that the card you draw will be a spade, and it is a spade, then you win $100. What is the expected financial value of playing this game?

- $1
- $25
- $100
- $400
**There is no way to calculate expected financial value in this game.**

Q4. Consider the following game: You flip a coin continuously until you get tails once. If you get no heads (tails on the first flip), then you are paid nothing. If you get one heads (tails on the second flip), then you are paid $2. If you two heads (tails on the third flip), then you are paid $4. If you get three heads (tails on the fourth flip), then you are paid $8. If you get four heads (tails on the fifth flip), then you are paid $16. And so on. The general rule is that, for any number n, if you get n heads before your first tails, then you are paid $2n (that is, 2 to the nth power dollars). What is the expected monetary value of this game?

- $2
- $4
- $8
- $16
**Infinite**

Q5. How much should you pay to play the game in the previous exercise?

- $0
- $2
- $4
- $8
- $16
- All of your savings
**Who knows?**;

### Week 4: Think Again III: How to Reason Inductively Coursera Quiz Answers

#### Quiz 1: Final Quiz

Q1. Deductive

validity comes in degrees.

- True
- False

Q2. Inductive strength is not defeasible.

- True
- False

Q3. Arguments

that apply generalizations to particular cases are

- Deductive
- Inductive
- Both deductive and

inductive - Neither deductive nor

inductive

Q4. An

argument that generalizes from a sample to a whole class is stronger (other

things being equal) when

- Its premises are

false - The sample is

smaller - The sample is unbiased
- All of the above
- None of the above

Q5. Specify the main

problem with the following generalization from a sample. There might be more

than one problem, but indicate the most important one.

A poll asked 100,000 randomly chosen people in Ecuador, Kenya, and Indonesia—

representing three continents—whether they own a winter coat. Less than 20%

said they did. Therefore, most people on Earth do not own a winter coat.

- The sample is too small
- The sample is biased
- The question is

slanted - Nothing is wrong with

this argument;

Q6. An

argument of the form “X% of Fs are Gs, a is an F, so a is probably NOT a G” is

strongest when X is:

- 10%
- 30%
- 50%
- 70%
- 90%

Q7. Consider this

argument: 90% of Chinese people like fish, and Manto is Chinese, so Manto

probably likes fish.

Would this argument be stronger or weaker if we added the

information that Manto is from a region of China where most people do not like

fish?

- Stronger
- Weaker
- Neither stronger nor weaker

Q8. If

two explanations are equal in all other respects, then

- The more conservative

explanation is better - The less conservative

explanation is better - Whether the

explanation is more or less conservative does not affect how good it is as an

explanation

Q9. Indicate which

explanatory virtue is lacking from this explanation:

Jing moved to Taiwan

because she wanted to.

- Falsifiability
- Conservativeness
- Power (or Breadth)
- Depth
- Modesty

Q10. Consider this

argument from analogy: I have visited many public gardens, and I almost always

enjoyed walking in them. I just moved to a new town with a public garden. I

have not visited it yet, but I know that it is similar in many ways to other

public gardens that I have visited. So I will probably enjoy walking in the new

public garden as well.

Would this argument from analogy become stronger, weaker, or neither if we

added a premise that the new public garden is a rock garden, but none of the

gardens that I visited before were rock gardens?

- Stronger
- Weaker
- Neither stronger nor weaker

Q11. Being a bird is

- Necessary but not

sufficient for being a swan - Sufficient but not

necessary for being a swan - Both necessary and

sufficient for being a swan - Neither necessary nor

sufficient for being a swan

Q12. Imagine that you buy

a new computer system with independent components including a new desktop

computer (with a CPU and a graphics card), new software, and a new monitor. You

want to play games on the new system, but it runs games very slowly. You assume

that the keyboard and mouse are not creating the problem; so, to figure out

what is making the system run so slowly, you experiment with combinations of

your old equipment with the new equipment. Here are your experiments and

results:

Experiment 1: New computer, new software, and new monitor — and it runs slowly.

Experiment 2: New computer, new software, and old monitor — and it runs slowly.

Experiment 3: New computer, old software, and new monitor — and it runs fast.

Experiment 4: New computer, old software, and old monitor — and it runs fast.

Experiment 5: Old computer, new software, and new monitor — and it runs slowly.

Experiment 6: Old computer, new software, and old monitor — and it runs fast.

Experiment 7: Old computer, old software, and new monitor — and it runs fast.

Experiment 8: Old computer, old software, and old monitor — and it runs fast.

Based on this data, which experiment shows that the new software is NOT SUFFICIENT

for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of these experiments

Q13. Imagine that you buy

a new computer system with independent components including a new desktop

computer (with a CPU and a graphics card), new software, and a new monitor. You

want to play games on the new system, but it runs games very slowly. You assume

that the keyboard and mouse are not creating the problem; so, to figure out

what is making the system run so slowly, you experiment with combinations of

your old equipment with the new equipment. Here are your experiments and

results:

Experiment 1: New computer, new software, and new monitor — and it runs slowly.

Experiment 2: New computer, new software, and old monitor — and it runs fast.

Experiment 3: New computer, old software, and new monitor — and it runs slowly.

Experiment 4: New computer, old software, and old monitor — and it runs fast.

Experiment 5: Old computer, new software, and new monitor — and it runs fast.

Experiment 6: Old computer, new software, and old monitor — and it runs fast.

Experiment 7: Old computer, old software, and new monitor — and it runs slowly.

Experiment 8: Old computer, old software, and old monitor — and it runs fast.

Based on this data, which experiment shows that the new computer is NOT

NECESSARY for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of these experiments

Q14. Imagine that you buy

a new computer system with independent components including a new desktop

computer (with a CPU and a graphics card), new software, and a new monitor. You

want to play games on the new system, but it runs games very slowly. You assume

that the keyboard and mouse are not creating the problem; so, to figure out

what is making the system run so slowly, you experiment with combinations of

your old equipment with the new equipment. Here are your experiments and

results:

Experiment 1: New computer, new software, and new monitor — and it runs slowly.

Experiment 2: New computer, new software, and old monitor — and it runs slowly.

Experiment 3: New computer, old software, and new monitor — and it runs fast.

Experiment 4: New computer, old software, and old monitor — and it runs fast.

Experiment 5: Old computer, new software, and new monitor — and it runs fast.

Experiment 6: Old computer, new software, and old monitor — and it slowly.

Experiment 7: Old computer, old software, and new monitor — and it runs fast.

Experiment 8: Old computer, old software, and old monitor — and it runs fast.

Based on this data, which experiment shows that the conjunction of the new

computer and the old monitor is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of the above;

Q15. Imagine that you buy

a new computer system with independent components including a new desktop

computer (with a CPU and a graphics card), new software, and a new monitor. You

want to play games on the new system, but it runs games very slowly. You assume

that the keyboard and mouse are not creating the problem; so, to figure out

what is making the system run so slowly, you experiment with combinations of

your old equipment with the new equipment. Here are your experiments and

results:

Experiment 1: New computer, new software, and new monitor — and it runs slowly.

Experiment 2: New computer, new software, and old monitor — and it runs slowly.

Experiment 3: New computer, old software, and new monitor — and it runs fast.

Experiment 4: New computer, old software, and old monitor — and it runs fast.

Experiment 5: Old computer, new software, and new monitor — and it runs slowly.

Experiment 6: Old computer, new software, and old monitor — and it runs fast.

Experiment 7: Old computer, old software, and new monitor — and it runs fast.

Experiment 8: Old computer, old software, and old monitor — and it runs fast.

Based on this data, which experiment shows that the conjunction of the new

software and the new monitor is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of these experiments

Q16. Imagine that you buy

a new computer system with independent components including a new desktop

computer (with a CPU and a graphics card), new software, and a new monitor. You

want to play games on the new system, but it runs games very slowly. You assume

that the keyboard and mouse are not creating the problem; so, to figure out

what is making the system run so slowly, you experiment with combinations of

your old equipment with the new equipment. Here are your experiments and

results:

- Experiment 1: New computer, new software, and new monitor — and it runs slowly.
- Experiment 2: New computer, new software, and old monitor — and it runs slowly.
- Experiment 3: New computer, old software, and new monitor — and it runs fast.
- Experiment 4: New computer, old software, and old monitor — and it runs fast.
- Experiment 5: Old computer, new software, and new monitor — and it runs slowly.
- Experiment 6: Old computer, new software, and old monitor — and it runs fast.
- Experiment 7: Old computer, old software, and new monitor — and it runs fast.
- Experiment 8: Old computer, old software, and old monitor — and it runs fast.

Based on this data, which experiment shows that the conjunction of the new

computer and the new software is not sufficient for the system to run slowly?

- Experiment 1
- Experiment 2
- Experiment 3
- Experiment 4
- Experiment 5
- Experiment 6
- Experiment 7
- Experiment 8
- None of these experiments

Q17. If

there is no case of a candidate (X) without the target (Y) in a data set, then

that data provides reason to believe the conclusion that the candidate (X) is

sufficient for the target (Y).

- True
- False

Q18. If

A is positively correlated with B, then

- A causes B
- B causes A
- A third thing causes

A and also causes B - Any of the other

answers might be true

Q19. Assume that A and B

are highly correlated. If A changes when you manipulate B, but B does not

change when you manipulate A, then which of the following is most likely?

Assume normal circumstances and no interfering factors.

- A causes B
- B causes A
- A third thing causes

both A and B - There is no causal

relation between A and B

Q20. When

dice are irregular so that the sides of the dice are not equal in size or

weight, then the most accurate way to determine the probability that they will

land with a certain side (such as 5) up is to use:

- A priori probability
- Statistical

probability - Subjective

probability;

Q21. If

the probability of a method of contraception working to prevent conception is

0.9, then what is the probability that it will not work?

- 0
- 0.1
- 0.5
- 0.9
- 1.0

Q22. Assume that you and

your neighbor will drive separately to work today. You have a 1% chance of getting

into an accident on the way to work today, and your neighbor has a 2% chance of

getting into an accident on the way to work today. Whether one of you has an

accident does not affect the probability that the other will have an accident

(because you drive opposite directions, the weather is not conducive to

accidents, etc.). What is the probability that both you and your neighbor will

have an accident on the way to work today?

- 0.00001
- 0.00002
- 0.01
- 0.02
- 0.1
- 0.2

Q23. Assume that there is

a 50% chance of rain on this Saturday in your city and a 50% chance of rain on

this Sunday in your city. If the rain storm hits your city, then it will be

likely to stay for more than one day, so there is an 80% chance of rain on this

Sunday, given that it rained on this Saturday. What is the probability that it

will rain on both this Saturday and this Sunday in your city?

- 0.04
- 0.2
- 0.4
- 0.5
- 0.8

Q24. Imagine that there is a 10% chance that you eat dinner

tonight before 6:00 p.m. and a 30% chance that you eat dinner tonight after

9:00 p.m. Assume that you eat dinner tonight only once. What is the probability

that you will eat dinner tonight either before 6:00 p.m. or after 9:00 p.m.?

- 0.03
- 0.1
- 0.3
- 0.37
- 0.4

Q25. Imagine that there is

a 60% chance of rain today in Delhi, India, and a 90% chance of rain today in

Paris, France. Also assume that the probabilities of rain today in Delhi and in

Paris are independent. What is the probability that it will rain today in either

Delhi or Paris (that is, in at least one of these cities)?

- 0.54
- 0.6
- 0.9
- 0.96
- 1.5

Q26. What

is the probability of rolling twelve at least once in a series of three fair

rolls of two six-sided dice in each roll?

- 1/36 + 1/36 + 1/36
- 35/36 + 35/36 + 35/36
- 35/36 x 35/36 x 35/36
- 1 – (35/36 x 35/36 x

35/36) - 1 – (1/36 x 1/36 x

1/36)

Q27. In the following game, you lay down $1 to bet that you

will pick a certain card in a fair draw from a standard deck. If you lose, then

you lose your $1. If you win, then you collect the gross amount indicated, so

your net gain is $1 less. What is the expected financial value of a bet where

you will win $2 if you draw a diamond?

- – $3/4
- – $2/4
- – $1/4
- $1/4
- $2/4

Q28. In the following

game, you lay down $1 to bet that you will pick a certain card in a fair draw

from a standard deck. If you lose, then you lose your $1. If you win, then you

collect the gross amount indicated, so your net gain is $1 less. What is the

expected financial value of a bet where you will win $52 if you draw a Queen of

Hearts?

- – $51/52
- – $1/52
- $0
- $1/52
- $51/52

Q29. In the following

game, you lay down $1 to bet that you will pick a certain card in a fair draw

from a standard deck. If you lose, then you lose your $1. If you win, then you

collect the gross amount indicated, so your net gain is $1 less. What is the

expected financial value of a bet where you will win $2 if you do NOT draw a

Spade?

- –$1/4
- $0
- $1/4
- $2/4
- $3/4

Q30. Whenever the expected

financial value of a bet is greater than $0, you should always take the bet,

regardless of its expected overall value.

- True
- False;

–

**Review: **

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