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...

Description
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?

Solution
a) The sequence of four movies has begun with D-D (that is given so we are not to
calculate probabilities for this beginning) and must end with another D. It can
be D-D-D-D or D-D-X-D, where X means a movie that is not of the...