4. The probability that a newborn baby is a boy is 0.52 . Find the probability that in a family of 6 children there are more girls than boys.
[3]

Step 1 ：Let n = 6, p = 0.48 (probability of having a girl), and calculate the probabilities for k = 4, 5, and 6 using the binomial probability formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Step 2 ：Calculate the probability of having 4 girls: \(P(X = 4) = C(6, 4) * 0.48^4 * (1-0.48)^{(6-4)} \approx 0.2153\)

Step 3 ：Calculate the probability of having 5 girls: \(P(X = 5) = C(6, 5) * 0.48^5 * (1-0.48)^{(6-5)} \approx 0.0795\)

Step 4 ：Calculate the probability of having 6 girls: \(P(X = 6) = C(6, 6) * 0.48^6 * (1-0.48)^{(6-6)} \approx 0.0122\)

Step 5 ：Add the probabilities of having 4, 5, and 6 girls to find the total probability: \(0.2153 + 0.0795 + 0.0122 \approx 0.307\)

Step 6 ：\(\boxed{\text{The probability that in a family of 6 children there are more girls than boys is approximately 0.307 or 30.7%}}\)