The probability of a boy or a girl being born is 1/2. For a family having only three children, what is the probability of having two girls and one boy?
Answer
(A)
Explanation
Each of the three children is independently a boy or a girl with probability \(\tfrac{1}{2}\), so all \(2^{3} = 8\) ordered outcomes are equally likely.
Two girls and one boy happens as GGB, GBG or BGG: \(\binom{3}{1} = 3\) outcomes, one for each choice of which child is the boy. The probability is \(\tfrac{3}{8}\).
The tempting \(\tfrac{1}{8}\) counts only one particular birth order.
Answer: A