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Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 44%. If they have three children, what is the probability that exactly one of their three children will have that trait? Round your answer to the nearest thousandth. Answer:

Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 44% 44 \% . If they have three children, what is the probability that exactly one of their three children will have that trait? Round your answer to the nearest thousandth.\newlineAnswer:

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Q. Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 44% 44 \% . If they have three children, what is the probability that exactly one of their three children will have that trait? Round your answer to the nearest thousandth.\newlineAnswer:
  1. Use binomial probability formula: Use the binomial probability formula: P(X=k)=C(n,k)⋅(p)k⋅(1−p)(n−k)P(X = k) = C(n, k) \cdot (p)^k \cdot (1-p)^{(n-k)} \newlineIdentify the values of nn, kk, and pp. \newlinen=3n = 3 (the number of children) \newlinek=1k = 1 (exactly one child with the trait) \newlinep=0.44p = 0.44 (the probability of a child having the trait)
  2. Identify values: Substitute the values into the binomial probability formula.\newlineP(X=1)=C(3,1)⋅(0.44)1⋅(1−0.44)(3−1)P(X = 1) = C(3, 1) \cdot (0.44)^1 \cdot (1-0.44)^{(3-1)}
  3. Substitute values: Calculate the binomial coefficient C(3,1)C(3, 1).
    C(3,1)=3!1!(3−1)!=31×2=32=1.5C(3, 1) = \frac{3!}{1! (3 - 1)!} = \frac{3}{1 \times 2} = \frac{3}{2} = 1.5
    Since the binomial coefficient must be an integer, we know there's a math error here. The correct calculation is:
    C(3,1)=3!1!(3−1)!=31×2=32=1.5C(3, 1) = \frac{3!}{1! (3 - 1)!} = \frac{3}{1 \times 2} = \frac{3}{2} = 1.5 which is incorrect because we should not have a decimal. The correct calculation is:
    C(3,1)=3!1!×2!=3×2×11×2×1=3C(3, 1) = \frac{3!}{1! \times 2!} = \frac{3 \times 2 \times 1}{1 \times 2 \times 1} = 3

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