Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 0.89 . If they have five children, what is the probability that exactly five of their five children will have that trait? Round your answer to the nearest thousandth. Answer:

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Identify values for formula: Identify the values of n, k, and p for the binomial probability formula. n represents the number of trials, which is the number of children, so n = 5. k represents the number of successes, which is the number of children with the trait, so k = 5. p represents the probability of success on a single trial, which is the probability of a child having the trait, so p = 0.89.Use binomial probability formula: Use the binomial probability formula: P(X = k) = C(n, k) * (p)^k * (1-p)^(n-k). Substitute n = 5, k = 5, and p = 0.89 into the formula to calculate the probability that exactly five of the five children will have the trait. P(X = 5) = C(5, 5) * (0.89)^5 * (1-0.89)^(5-5).Calculate C(5, 5): Calculate the value of C(5, 5). C(5, 5) = 5! / 5! (5 - 5)! = 1 because the factorial of zero (0!) is 1 and any number factorial divided by itself is 1.Simplify probability formula: Simplify the probability formula with the calculated values. P(X = 5) = 1 * (0.89)^5 * (1-0.89)^(5-5). Since (1-0.89)^(5-5) is (0.11)^0, and any number to the power of zero is 1, this term simplifies to 1.Calculate (0.89)^5: Calculate (0.89)^5. (0.89)^5 = 0.89 * 0.89 * 0.89 * 0.89 * 0.89.Perform calculation for (0.89)^5: Perform the calculation for (0.89)^5. (0.89)^5 ≈ 0.5584059449.Multiply values for probability: Multiply all the values together to find the probability. P(X = 5) = 1 * 0.5584059449 * 1. P(X = 5) ≈ 0.5584059449.Round answer to nearest thousandth: Round the answer to the nearest thousandth. P(X = 5) ≈ 0.558.

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