Q7. 10 marks 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. Use the Bayes' law on conditional probabilities to answer the following. (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 answers in parts a) and b) and explain the relation between them. 3 (d) What sort of biases are subjects expected to exhibit when they use Bayes' Law? Which elements of the problem are they likely to give less attention to in their answers, relative to the correct application of Bayes' Law