Mean, variance, and median on World Series

Question

Teams A and B play in a best of 7 series. Team B has a 45% chance of winning each game. Find the mean, variance, and median.

Answer 1

You need to first find the probability that each team wins in 4, 5, 6, 7 games.

This can be done using the binomial theorem plus a little logic.

P(A wins in 4 games) = (.55)^4

P(B wins in 4 games) = (.45)^4

P(A wins in 5 games) = 4(.55)^4 (.45), since A must lose exactly one of the first 4 games.

etc

Once you find these 8 probabilities, calculate the mean and variance of X using the standard formulas.

The median of X should be obvious.