Bayes's theorem on conditional probabilities states that, if P(B) is not 0, then
P(A given B) =
P(B given A) × P(A)
P(B)
.
There are two bowls of cookies. Bowl Alpha has 7 chocolate chip cookies and 10 peanut butter cookies. Bowl Beta has 10 chocolate chip cookies and 10 peanut butter cookies. Jerry selects a bowl at random and chooses a cookie at random from that bowl. Leave your answers as fractions.
(a) What is the probability that he chooses bowl Alpha?
1/2
(b) What is the probability that he gets a chocolate chip cookie given that he chooses from bowl Alpha?
7/17
(c) It can be shown that the probability that he gets a chocolate chip cookie is 31/68. What is the probability that he chose from bowl Alpha given that he got a chocolate chip cookie? Note: In this situation, Bayes's theorem says
P(Alpha given Chocolate) =
P(Chocolate given Alpha) × P(Alpha)
P(Chocolate)
