Question

Consider the composition of a 3-child family in which the children were born at different times but a girl is as likely as a boy at each birth. What is the probability that the oldest child and the youngest child are of the same gender

Answer 1

$A-1st\,\,and\,\,3rd\,\,child\,\,of\,\,the\,\,same\,\,gender\\P\left( A \right) =P\left( 1st\,\,boy, 3rd\,\,boy \right) +P\left( 1st\,\,girl, 3rd\,\,girl \right) =\\=\frac{1}{2}\cdot \frac{1}{2}+\frac{1}{2}\cdot \frac{1}{2}=0.5$