Question

Two teams A and B play a series ofgames until one team wins four games. Assume that the outcomes of the gamesare independent and that the probability that A wins any one game isp. Whatis the probability that the series lasts five games?

Answer 1

Answer:

Step-by-step explanation:

Please find the answer in this photo below

Hope it will find you well

Answer 2

Since we assume the outcome of the games are independent and the probability that A wins any one game is p. We will have that:

The probability that:

Team A wins in 5 games = $p^{4} (1p)$

Team B wins in 5 games = $p(1p)^{4}$

Since there are 4 ways each team can win in 5 games, the probability that the series last 5 games is:

$4[p^{4} (1p)+p(1p)^{4} ]$

Thus, the answer is:

$4[p^{4} (1p)+p(1p)^{4} ]$