Question: Mr. Gorfin is a movie buff who watches movies regularly. His son has observed that whether Mr. Gorfin watches a drama or not depends on the previous two movies he has watched with the following probabilities: 7/8 if the last two movies he watched were both dramas, 1/2 if exactly one of them was a drama, and 1/8 if none of them was a drama.
(a) Mr. Gorfin watched four movies last weekend. If the first two were dramas, what is the probability that the fourth one was a drama as well?
(b) What is the long-run probability that Mr. Gorfin will watch two dramas in a row?