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I have a few exam review questions that I don't know how to solve. Maybe someone can help me out.
Two hockey teams play a best-of-seven series (play until a team wins a total of 4 games)
Assume team A has a probability of 3/4 of beating team B.
Assume the results of the games are independent
What is the probability that all seven games will be played in the series
The series lasts $7$ games precisely if the first $6$ games are evenly split between the two teams. So we want the probability that Team A wins $3$ of the first $6$ games and loses $3$. The probability of that is $$\binom{6}{3}\left(\frac{3}{4}\right)^3\left(\frac{1}{4}\right)^3.$$
