1Suppose the unconditional probability of Event X, written Pr(X), is 0.83 and the unconditional probability of Event Y, written Pr(Y), is 0.6. If the two events are independent, what is the conjunction Pr(X & Y)?
0.498
2Suppose the unconditional probability of Event X, written Pr(X), is 0.83 and the unconditional probability of Event Y, written Pr(Y), is 0.6. If the two events are not independent, and the conditional probability Pr(X|Y) = 0.39, what is the conjunction Pr(X & Y)?
0.234
3I have a deck of 52 cards. What is the probability that the top card is a seven or a heart?
[Keep in mind that there are four suits (clubs, spades, hearts and diamonds) in a deck and 13 different types of cards (2-10, jack, queen, king, and ace) in each suit]
16/52
4Dr. Howard wants to know the probability that his children will strike him with plastic swords on Halloween. He does not know this directly, but he can calculate it indirectly. He knows that this probability depends on what costume his children wear. If they dress as characters from Star Wars, the probability that Dr. Howard will be hit with swords is 92%. If they wear any other costume, the probability that Dr. Howard will be hit with swords is 20%. He also knows that the probability that his children will dress as Star Wars characters is 60%. Using the total probability rule, what is the probability that Dr. Howard will be hit with plastic swords on Halloween?
0.632
5I have a shuffled deck of cards. Consider the following outcomes:
i. The top card is a spade.
ii. The bottom card is the queen of hearts.
iii. The bottom card is a black suit (spades or clubs).
iv. The top card is the ace of spades.
v. The bottom card is not a diamond.
Which of the above outcomes are mutually exclusive?
ii. and iii.
6Which term captures the mistake of assuming that events are dependent when in fact they are independent?
The Gambler’s Fallacy
7Dr. Gregg is tested for a disorder, and the test comes back negative (indicating he has the disorder). The doctors tell him that the test comes back positive for 90% of people who have the disorder and only 5% of people who do not have the disorder. Dr. Gregg doesn’t know the base rate (the percentage of the population that has the disorder), but he assumes he definitely has the disorder (basically, he assumes the probability that he has the disorder is 1). For which disorder will Dr. Gregg’s guess be furthest from the actual probability that he has the disorder?
Thinking Like an Economist Disease (1% of the population suffers from this disorder)
8Dr. Gregg is tested for diabetes, and the test comes back positive. Tests are not always right, so the probability that Dr. Greg has diabetes is not 100%. The doctors tell him only that the test comes back positive for 95% of people who have diabetes, and from this information Dr. Gregg assumes he definitely has diabetes (probability is 1). For which diabetes test will Dr. Gregg’s guess be furthest from the actual probability that he has diabetes?
Test A: This test comes back positive for 95% of people who don’t have diabetes.
9Which of the following best describes the Conjunction Fallacy?
People tend to overestimate AND probabilities (Pr(A & B))
10Which of the following examples illustrates availability bias?
I think that large earthquakes are more common than tornadoes because I live in an area that gets lots of earthquakes and very few tornadoes.