Basketball team A won 5 out of 7 games at home and 2 out of 7 games away against team B. In the playoffs, team A won 2 games at home and 1 away. Estimate the probability of this happening?

Answer 1

This is a Binomial Distribution. Assuming teams A and B have equal ability, and that A is equally likely to win at home as away, the probability that A wins any particular game is 1/2.

Also, you did not say how many playoffs games there were. Did team win 3 out of 3 playoff games? That is what I am assuming in this answer.

So p = 1/2, 1-p = 1/2

In general P(r successes out of n trials) = _nC_r p^r (1-p)^n-r

P(A wins 5 out of 7 home games) = ₇C₅ (1/2)⁵ (1/2)² = ₇C₅ (1/2)⁷

P(A wins 2 out of 7 away games) = ₇C₂ (1/2)² (1/2)⁵ = ₇C₂ (1/2)⁷

P(A wins 3 out of 3 playoff games) = ₃C₃ (1/2)³ = (1/2)³

Total Probability = ₇C₅ (1/2)⁷ * ₇C₂ (1/2)⁷ * (1/2)³ ≈ .0034