You feel that the probability of a head on a toss of a particular coin is either

.4, .5, or .6. Your prior probabilities are P (A) = .1, P(.5) = .7, P(.6) = .2.

You toss the coin three times and obtain one head and two tails. What are the posterior probabilities? If you then toss the coin three more times and once again obtain one head and two tails, what are the posterior probabilities?

Also compute the posterior probabilities by pooling the two samples and revising the original probabilities just once; compare with your previous answer.