Question

A family has four children find the probability that the family has equal number of sons and daughter.

Answer 1

Let $X=$ the number of boys:$X\sim Bin(n, p).$

Given $n=4, p=0.5, q=1-p=0.5$

$$P(X=2)=\dbinom{4}{2}(0.5)^{2}(0.5)^{4-2}=\dfrac{3}{8}=0.375$$