Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ . What is the probability of having exactly two girls and three boys?
A) 0.0312
B) 0.3125
C) 0.6252
D) 0.0625

Question

Quizplus · Accepted Answer

The probability of having exactly two girls and three boys in a family of five children, where each child is equally likely to be a boy or a girl, can be calculated using the binomial probability formula. The formula for the binomial probability of getting exactly k successes (in this case, girls) in n trials (children) is $P(k; n, p) = \binom{n}{k} p^k (1-p)^{n-k}$, where $p$ is the probability of success (having a girl), $n$ is the total number of trials, and $k$ is the number of successes. Here, $p = \frac{1}{2}$, $n = 5$, and $k = 2$. Thus, the probability is $\binom{5}{2} \left(\frac{1}{2}\right)^2 \left(\frac{1}{2}\right)^{3} = 10 \times \frac{1}{32} = \frac{10}{32} = 0.3125$.

Suppose That a Family Has 5 Children and That the Probability