If the probability that the Islanders will beat the Rangers in a game is 61%, what is the probability that the Islanders will win exactly five out of seven 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  61%, what is the probability that the Islanders will win exactly five out of seven 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). Here, n is the number of trials, k is the number of successes, and p is the probability of success on a single trial. For this problem: n = 7 (since there are seven games), k = 5 (since we want to find the probability of exactly five wins), p = 0.61 (since the probability of the Islanders winning a single game is 61%).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)!. Substitute n = 7 and k = 5 into the formula: C(7, 5) = 7! / 5! (7 - 5)! = 7 * 6 / 2 * 1 = 42 / 2 = 21.Calculate probability of five wins: Calculate the probability of exactly five wins P(X = 5). Using the binomial probability formula: P(X = 5) = C(7, 5) * (0.61)^5 * (1 - 0.61)^(7 - 5) Substitute the values we have calculated: P(X = 5) = 21 * (0.61)^5 * (0.39)^2.Solve probabilities: Solve (0.61)^5 and (0.39)^2. Calculate (0.61)^5: (0.61)^5 = 0.61 * 0.61 * 0.61 * 0.61 * 0.61 ≈ 0.088567. Calculate (0.39)^2: (0.39)^2 = 0.39 * 0.39 ≈ 0.1521.Multiply values for probability: Multiply all the values together to find the probability P(X = 5). P(X = 5) = 21 * 0.088567 * 0.1521 ≈ 0.282711 * 0.1521 ≈ 0.043004.Round to nearest thousandth: Round the answer to the nearest thousandth. The probability P(X = 5) rounded to the nearest thousandth is: 0.043.

If the probability that the Islanders will beat the Rangers in a game is $61 \%$ , what is the probability that the Islanders will win exactly five out of seven 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 61% 61 \% 61%, what is the probability that the Islanders will win exactly five out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.\newlineAnswer:

If the probability that the Islanders will beat the Rangers in a game is $61 \%$ , what is the probability that the Islanders will win exactly five out of seven games in a series against the Rangers? Round your answer to the nearest thousandth. $\newline$ Answer: