There are two boxes, B1 and B2. Box B1 contains 4 red balls and 2 green balls and box B2 contains 4 green and two red balls. Nature selects box B1 with a probability 1/3 and box B2 with a probability 2/3. One of the two boxes is selected at random and a ball is selected at random from it. Suppose that the randomly ball selected is red.
(a) What is the probability that it was selected from box B1?
(b) What is the probability that it was selected from box B2?
(c) Compare the results in parts (a) and (b) and explain the answer.
(d) Suppose that subjects neglect base rates as they often do in the evidence on human behavior. What is the answer that such subjects are likely to give to part (a)?