Question

The percentage of wins for a basketball team going into the playoffs was 90% last season.

a. What is the probability that the team sweeps (4-0) the initial best-of-7 playoff series?

b. What is the probability that the team wins the initial best-of-7 playoff series?

Answer 1

Number of Trials (n) = 7

Probability of success (wining percentage) = 0.9

Probability of loss = 1 - 0.9 = 0.1

a):

The probability of wining 4 consecutive games from the beginning without losing any is:

$P=4{C_4}\times (0.9)^{4}\times (0.1)^{0}$

$P=0.9\times 0.9\times 0.9\times0.9=0.6561$

b):

Probability that the team wins the initial best-of-7 playoff series is:

$P=7{C_7}\times (0.9)^{7}\times (0.1)^{0}$

$P=0.9\times 0.9\times 0.9\times0.9\times 0.9\times 0.9\times0.9=0.4783$