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 three girls and two boys?
A) 0.6252
B) 0.0313
C) 0.3125
D) 0.0625

Question

Quizplus · Accepted Answer

The probability of having exactly three girls and two boys in a family of five children, with each child being equally likely to be a boy or a girl, can be calculated using the binomial probability formula. The formula for exactly k successes (in this case, girls) out of n trials (children) is $C(n, k) \times p^k \times (1-p)^{n-k}$, where $C(n, k)$ is the number of combinations of n items taken k at a time, and p is the probability of success (having a girl) on any given trial. Here, $n = 5$, $k = 3$, and $p = \frac{1}{2}$, so the probability is $C(5, 3) \times \left(\frac{1}{2}\right)^3 \times \left(\frac{1}{2}\right)^2 = 10 \times \frac{1}{32} = \frac{10}{32} = 0.3125$.

Suppose That a Family Has 5 Children and That the Probability