The Dallas Mavericks and the Golden State Warriors are two teams in the National Basketball Association. Dallas and Golden State will play multiple times over the course of an NBA season. Assume that the Dallas Mavericks have a 25% probability of winning each game against the Golden State Warriors.
a. Construct a simulation model that uses the negative binomial distribution to simulate the number of games Dallas would lose before winning four games against the Golden State Warriors.
b. Now suppose that the Dallas Mavericks face the Golden State Warriors in a best-of seven playoff series in which the first team to win four games out of seven wins the series. Using the simulation model from part (a), estimate that probability that the Dallas Mavericks would win a best-of-seven series against the Golden State Warriors.