A couple has 2 children. The probability that both children are boys if the older one is a boy is
Options:
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
Official Answer Key:
C
Step-by-Step Solution & Explanation
• Conditioning on “the older child is a boy” fixes the older child’s sex; only the younger child’s sex is random, independent of the older child, with P(boy) = 1/2.
• P(both boys | older is a boy) = P(younger is a boy) = 1/2.
• (This differs from the classic “at least one is a boy” version, which gives 1/3 — here the condition specifically fixes the older child, removing that ambiguity.)
• Final Answer: (C) 1/2
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.