Answer to Question #263430 in Statistics and Probability for xoxo

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

p=0.90

q=0.10

n=7

a. $0.90 \times 0.90 \times 0.90 \times 0.90 = 0.6561$

The probability that the team sweeps (4-0) the initial best-of-7 playoff series is 0.6561

b.

$P(X=x) = C^7_x \times 0.90^x \times 0.1^{7-x} \\ P(wins) = P(X≥4) = P(X=4) + P(X=5) +P(X=6) +P(X=7) \\ = C^7_4 \times 0.90^4 \times 0.1^{7-4} + + C^7_5 \times 0.90^5 \times 0.1^{7-5 } + + C^7_6 \times 0.90^6 \times 0.1^{7-6} + + C^7_7 \times 0.90^7 \times 0.1^{7-7} \\ = 0.0229635 + 0.1240029 + 0.3720087 + 0.4782969 \\ = 0.997272$

The probability that the team wins the initial best-of-7 playoff series is 0.997272