chapter 17 Flashcards
When you experience a coincidence, which of the following interpretations is appropriate?
a. If an event has a million to one chance, it is expected to happen to 290 people in the U.S. in a given day, on average (because the U.S. population is 290 million).
b. It is not unlikely that something surprising will happen to someone, somewhere, someday.
c. There is a big difference between the probability of a rare event happening to someone somewhere, and the probability of a rare event happening to a specifically named individual.
d. All of the above.
D
- About how many people would need to be gathered together to be at least 50% sure that two of them will share the same birthday (the same day of the year, not necessarily the same year)?
a. 4
b. 23
c. 183
d. 2,300 or more
B
- Which of the following lottery combinations (6 numbers from 1-30, no repeats allowed) is the least likely to come up as a winning ticket?
a. 2, 10, 23, 27, 30, 11
b. 1, 2, 3, 4, 5, 6
c. 11, 19, 14, 12, 17, 15
d. All of the above are equally unlikely.
D
Which of the following coincidences reflects a truly improbable event, if interpreted properly?
a. My next-door neighbor won the lottery! I was only one house away from becoming rich!
b. Wow, what are the chances that I’d be on the same flight as Bill Cosby? Unbelievable!
c. I heard there’s a guy in Pennsylvania who won the lottery twice; that lottery must be rigged.
d. None of the above.
D
- Which of the following beliefs are examples of the gambler’s fallacy?
a. Random events are self-correcting. (For example if you are losing, believing that your luck is about to turn around.)
b. The long-run frequency of an event should apply in the short term as well. (For example, “He’s a 90% free throw shooter, and he’s already missed 2 out of 3 tonight. There’s no way he’s going to miss this next one.”)
c. Knowledge of one event will help predict the next event, even though the events are independent. (For example, you may hear someone at the craps table saying to the person rolling the dice, “You’re on a roll! Don’t stop now!”)
d. All of the above.
D
- In which of the following situations would the gambler’s fallacy not apply?
a. When the events are not independent.
b. When knowledge of one outcome affects the probability of the next one.
c. Both a) and b).
d. Neither a) nor b); the gambler’s fallacy holds whenever gambling is going on. That’s how casinos stay in business.
C
- Which of the following is needed in order to determine the probability of a positive test result being accurate?
a. The base rate.
b. The sensitivity of the test.
c. The specificity of the test.
d. All of the above.
D
- Which probability is larger for a randomly selected woman from the general population: The probability of having breast cancer given that the woman has a positive mammogram, or the probability of a positive mammogram given that the woman has breast cancer?
a. The probability of having breast cancer given that the woman has a positive mammogram.
b. The probability of a positive mammogram given that the woman has breast cancer.
c. The probabilities are the same.
d. Not enough information to tell.
B
- What is meant by a test result that is a false positive?
a. You have the disease but the test results were negative.
b. You don’t have the disease but the test results were positive.
c. You test positive for a different disease than the one they thought you had.
d. None of the above.
B
- Which of the following describes the ‘specificity’ of a test for a certain disease?
a. The probability that you are likely to have a specific disease, without any knowledge of your test results.
b. The proportion of people who correctly test positive when they actually have the disease.
c. The proportion of people who correctly test negative when they don’t have the disease.
d. All of the above.
C
- Which of the following problems can arise when intuition differs from relative frequency?
a. Always thinking that a coincidence has a low chance of occurring.
b. The gambler’s fallacy.
c. Confusion of the inverse.
d. All of the above.
D
- Which of the following would be true if people made decisions based on maximizing their expected monetary return?
a. People wouldn’t buy lottery tickets.
b. People wouldn’t buy insurance.
c. People wouldn’t participate in sports betting.
d. All of the above.
D
