Probability question

Question

Suppose the NBA final is between Heat and Mavericks where a team wins the series when it wins k number of games. NB The NBA does not allow draws. Suppose the Heats has p as a probability to win each game. What is the expected number and variance of games that are played when k =5

Answer 1

Since there are no draws, the outcomes are wins/losses which means that the binomial distribution is a good way to model this assuming that the individuals matches are independent (this may or may not be a good assumption in real life, but lets roll with it).

The expected value for the binomial is k*p where k is the number of trials (games in our case) and p is the probability of success. The variance of the binomial is kp(1-p). In your case, k=5, so the expected number of games would be 5p and the variance would be 5p(1-p).