Question

If the probability that the Islanders will beat the Rangers in a game is 5/9, what is the probability that the Islanders will win exactly three out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.

Answer 1

• 0.235

Explanation:

Probability of win is:

• p(w) = 5/9 = 0.555

Probability of loss is:

• p(l) = 1 - p(w) = 1 - 0.555 = 0.445

Combinations of 3 wins out of 7 games is:

• 3C7 = 7!/3!4! = 7*6*5/2*3 = 35

Required probability:

• P = 35*(0.555)³(0.445)⁴ = 0.235 (rounded)