Discussion
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
The probability is 3/8.
Three children give 23 = 8 equally likely sequences. Exactly two girls and one boy occur in GGB, GBG and BGG, so
\[ P = \binom{3}{2}\left(\tfrac{1}{2}\right)^{3} = \tfrac{3}{8} \]
1/8 is the probability of one particular order, which forgets that the boy can be first, second or third. 1/2 and 1/4 do not follow from the count.
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