A couple has 2 children. The probability that both children are boys if the older one is a boy is: A. 1/4 B. 1/3 C. 1/2 D. 1

GATE 2017 · General Aptitude · Probability · medium

Answer: The probability that both children are boys, given the older one is a boy, is 1/2. Answer: C.

1. Define the full sample space: All four outcomes for (older child, younger child) are equally likely. P(each) = 1/4.
2. Apply the condition: older child is a boy: Conditioning event: older is a boy. Reduced sample space = {BB, BG}.
3. Compute conditional probability: P(BB | older=B) = (1/4) / (1/2) = 1/2.