Answer:
0.0021 or 0.21%
Step-by-step explanation:
To find the probability that the Islanders will win exactly six out of six games in a series against the Rangers, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n = total number of games in the series (6 games)
- k = number of games the Islanders win (6 games)
- p = probability that the Islanders will win a game (0.37)
- (n choose k) = n! / k!(n-k)!
Plugging in the values:
P(X = 6) = (6 choose 6) * 0.37^6 * (1-0.37)^(6-6)
P(X = 6) = 1 * 0.37^6 * (1-0.37)^0
P(X = 6) = 0.37^6
P(X = 6) ≈ 0.0021
Therefore, the probability that the Islanders will win exactly six out of six games in a series against the Rangers is approximately 0.0021, or 0.21% when rounded to the nearest thousandth.
