Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 41%. If they have four children, what is the probability that at most one of their four children will have that trait? Round your answer to the nearest thousandth. Answer:

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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  41%. If they have four children, what is the probability that at most one of their four children will have that trait? Round your answer to the nearest thousandth. Answer:

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Understand and Identify Formula: Understand the problem and identify the binomial probability formula for at most one success. The problem asks for the probability that at most one of the four children will have the genetic trait. This means we need to calculate the probability of having exactly one child with the trait and the probability of having no children with the trait, then add these probabilities together. 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, and p is the probability of success on a single trial.Calculate Probability of No Children: Calculate the probability of having no children with the trait (k = 0). Using the binomial probability formula, we substitute n = 4, k = 0, and p = 0.41. P(X = 0) = C(4, 0) * (0.41)^0 * (1-0.41)^(4-0) P(X = 0) = 1 * 1 * (0.59)^4Calculate Value of (0.59)^4: Calculate the value of (0.59)^4. (0.59)^4 = 0.59 * 0.59 * 0.59 * 0.59 = 0.12117381Calculate Probability of One Child: Calculate the probability of having exactly one child with the trait (k = 1). Using the binomial probability formula, we substitute n = 4, k = 1, and p = 0.41. P(X = 1) = C(4, 1) * (0.41)^1 * (1-0.41)^(4-1) P(X = 1) = 4 * 0.41 * (0.59)^3Calculate Value of (0.59)^3: Calculate the value of (0.59)^3. (0.59)^3 = 0.59 * 0.59 * 0.59 = 0.205379Multiply Values for P(X = 1): Multiply the values together to find P(X = 1). P(X = 1) = 4 * 0.41 * 0.205379 = 0.33723836Add Probabilities for Total: Add the probabilities of P(X = 0) and P(X = 1) to find the total probability of at most one child with the trait. P(at most one) = P(X = 0) + P(X = 1) = 0.12117381 + 0.33723836 = 0.45841217Round to Nearest Thousandth: Round the answer to the nearest thousandth. P(at most one) = 0.458

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