Suppose that it is believed that the proportion of consumers in a large popu¬

lation that will purchase a certain product is either .2, .3, .4, or .5. Further¬

more, the prior probabilities for these four values are P(.2) = .2, P(.3) = .3, P(A) = .3, and P (.5) = .2. A sample of size 10 is taken from the population, and of the ten consumers, 3 state that they will buy the product. What are the posterior probabilities? In calculating the posterior probabilities, what assumptions did you need to make?