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 are of the same gender

Answer 1

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