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If the probability that the Islanders will beat the Rangers in a game is 29%, what is the probability that the Islanders will win exactly six out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.

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7 votes

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.

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