2019 September 23,
Carleton College, Joshua R. Davis
A: Suppose that P(A) = P(B) = 0.3 and P(A | B) = 0.5. Find P(A union B).
B: Section 2.11 Exercise 1.
C: Section 2.11 Exercise 3.
D: Section 2.11 Exercise 17.
E: Section 2.11 Exercise 53.
F: A crime victim is beaten over the head with a laptop computer. (Don't worry; he's fine now.) When questioned about the laptop, a witness identifies it as one manufactured by Apple, which commands 7% of the laptop market. A psychologist consulted by the police estimates that eye witnesses can recall such details correctly about 80% of the time. What is the probability that the laptop was an Apple?
G: Another psychologist consulted in the case above raises an issue of cognitive bias: People tend to see what they expect to see. When people see a PC (non-Apple) laptop, they correctly recall so 80% of the time. But when people see an Apple laptop, they correctly recall so less than 80% of the time (because some of them actually see a PC laptop, because that is what they expect to see, because PCs are common). How does this insight affect the answer to the previous problem?