Answer:
0.003
Explanation:
To calculate the probability of the Islanders winning exactly six out of seven games in a series against the Rangers, we can use the binomial probability formula.
To calculate the probability of the Islanders winning exactly six out of seven games in a series against the Rangers, we can use the binomial probability formula.The binomial probability formula is given by:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of getting exactly k successes.
n is the total number of trials.
k is the number of successful outcomes.
p is the probability of success in a single trial.
C(n, k) is the number of combinations of n items taken k at a time.
In this case, n = 7 (since there are seven games in the series), k = 6 (since we want exactly six wins), and p = 0.29 (the probability of the Islanders winning a single game).
Using the formula, we can calculate the probability as follows:
P(X = 6) = C(7, 6) * 0.29^6 * (1 - 0.29)^(7 - 6)
C(7, 6) = 7 (since there are 7 ways to choose 6 out of 7 games)
P(X = 6) = 7 * 0.29^6 * (1 - 0.29)^(7 - 6)
= 7 * 0.000708624 * 0.71
= 0.003451992
Rounding to the nearest thousandth, the probability that the Islanders will win exactly six out of seven games in a series against the Rangers is approximately 0.003.