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

Answer:

0.014

Step-by-step 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.

$P(X=x) = \frac{n!}{(n-x)!x!}*p^ x*(1-p)^{(n-x)}$

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.