Question 10.1: A family has two children. Find the probability that they ar......

The sample space for a family of two children is S = {(g, g), (g, b), (b, g), (b, b)}. The event E where is at least one girl in the family is given by E = {(g, g), (g, b), (b, g)}, and the event G that both are girls is G = {(g, g)}, so we will determine the conditional probability P(G|E)) that both children are girls given that there is at least one girl in the family:

P(EG) = P(G) = P(g, g) = {}^{1}/_{4}

P(E) = {}^{3}/_{4}

P(G|E) = \frac{P(EG)}{P(E)}=\frac{{}^{1}/_{4}}{{}^{3}/_{4}}={}^{1}/_{3}