At the NBA playoff finals, the championship is awarded in a best-out-of-seven series of games, i.e. the first team to reach four wins is the champion. Assume that in each game, the two teams, say A and B, have the same probability of winning.

(i) What is the probability that team A wins the trophy? (You should be able to guess the answer by symmetry. Then you may verify formally that this is correct.)

(ii) What is the probability that team A wins the trophy if we know that team B has won the first game?

(iii) What is the probability that the series lasts for k games (for k = 4, 5, 6, 7)?

(iv) If we know that the series was decided after k games, what is the probability that team B won the championship? Again, try to give an intuitive answer to this question without doing any calculations, and then check that this is correct (establishing in particular that the probability is the same for any value of k).

(v) What is the expected number of games in the series?