If the probability that the Islanders will beat the Rangers in a game is 18%, what is the probability that the Islanders will win exactly one out of six games in a series against the Rangers? Round your answer to the nearest thousandth. Answer:

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If the probability that the Islanders will beat the Rangers in a game is  18%, what is the probability that the Islanders will win exactly one out of six games in a series against the Rangers? Round your answer to the nearest thousandth. Answer:

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Identify Formula and Values: Identify the binomial probability formula and the values of n, k, and p. The binomial probability formula is P(X = k) = C(n, k) * (p)^k * (1-p)^(n-k), where: - n is the number of trials, - k is the number of successes, - p is the probability of success on a single trial. For this problem: n = 6 (since there are six games), k = 1 (since we want to find the probability of exactly one win), p = 0.18 (since the probability of the Islanders winning a game is 18%).Calculate Binomial Coefficient: Calculate the binomial coefficient C(n, k). The binomial coefficient C(n, k) is calculated using the formula n! / k! (n - k)!. For n = 6 and k = 1, we have: C(6, 1) = 6! / 1! (6 - 1)! = 6 / 1 * 5! = 6 / 120 = 1/20 = 0.05.Calculate Probability of One Win: Calculate the probability of exactly one win using the binomial probability formula. Substitute n = 6, k = 1, and p = 0.18 into the formula P(X = k) = C(n, k) * (p)^k * (1 - p)^(n - k): P(X = 1) = C(6, 1) * (0.18)^1 * (1 - 0.18)^(6 - 1).Solve Probability Expression: Solve the probability expression. First, calculate (0.18)^1, which is simply 0.18. Next, calculate (1 - 0.18)^(6 - 1), which is (0.82)^5. (0.82)^5 = 0.82 * 0.82 * 0.82 * 0.82 * 0.82 ≈ 0.32890368. Now, multiply C(6, 1), (0.18)^1, and (0.82)^5 together: P(X = 1) = 0.05 * 0.18 * 0.32890368 ≈ 0.00296553.Round to Nearest Thousandth: Round the answer to the nearest thousandth. P(X = 1) ≈ 0.00296553 rounded to the nearest thousandth is 0.003.

If the probability that the Islanders will beat the Rangers in a game is $18 \%$ , what is the probability that the Islanders will win exactly one out of six games in a series against the Rangers? Round your answer to the nearest thousandth. $\newline$ Answer:

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If the probability that the Islanders will beat the Rangers in a game is $18 \%$ , what is the probability that the Islanders will win exactly one out of six games in a series against the Rangers? Round your answer to the nearest thousandth. $\newline$ Answer: