1) Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the teams is stronger than the other and wins each game with probability 0.6, independant of the outcomes of the other games. Find the probability that the stronger team wins the series in exactly i games. Do it for i=4,5,6,7. Compare the probability that the stronger team wins with the probability that it would win a 2-out-of-3 series.
2) Suppose in the problem above, that the two teams are evenly matched and each has probability 1/2 of winning each game. Find the expected number of games played.
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