Question

If the probability that the Islanders will beat the Rangers in a game is 0.38, what is the probability that the Islanders will win at least six out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.

Answer 1

0.014

Explanation:

The probability that the Islanders will win at least 6 out of seven is the probability of them winning exactly 6 games, P(X=6), added to the probability of them winning all seven games, P(X=7).

This problem can be treated as a binomial probability model with probability of success p = 0.38 in each of n = 7 games.

`P(X=x) = (n!)/((n-x)!x!)*p^ x*(1-p)^((n-x))`

Thus:

`P(X=6) = 7*0.38^6*0.62\\P(X=6) =0.01307\\P(X=7) = 0.38^7\\P(X=7) =0.00114`

The probability is:

`P(X\geq 6) = 0.01307+0.00114\\P(X\geq 6) = 0.014`

The probability that the Islanders will win at least six out of seven games in a series against the Rangers is 0.014.