Question

The Wilson family had 7 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had at least 5 girls? at most 5 girls? Round your answers to 3 decimal places.

Answer 1

To find the probability that the Wilson family had at least 5 girls, we can use the binomial probability formula and calculate the probabilities of having exactly 5, 6, and 7 girls. Then, we add these probabilities together.

Step-by-step explanation:

To find the probability that the Wilson family had at least 5 girls, we can use the binomial probability formula. Let's consider the probability of having exactly 5 girls, exactly 6 girls, and exactly 7 girls. Then, we can add these probabilities together:

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7)

Using the binomial probability formula, where n = 7 (total number of children) and p = 0.5 (probability of a child being a girl), we can calculate the probabilities:

P(X = 5) = C(7, 5) × (0.5)⁵ × (1-0.5)⁽⁷⁻⁵⁾

P(X = 6) = C(7, 6) × (0.5)⁶ × (1-0.5)⁷⁻⁶⁾

P(X = 7) = C(7, 7) × (0.5)⁷ × (1-0.5)⁷⁻⁷⁾

Finally, we add these probabilities together to find the probability of having at least 5 girls.