Mr Gorfin Is A Movie Buff Who Watches Movies Regularly His Son Has Observed That Whe 2307608

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?

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