Difficulty: Easy · Puzzle 3 of 6 · Topic: Probability Puzzles
A family has two children. Given that at least one child is a boy, what is P(both are boys)? Assume boy/girl equally likely and independent.
Write conditioned sample space explicitly.
1) Unconditioned equiprobable outcomes: BB, BG, GB, GG.
2) Condition 'at least one boy' removes GG.
3) Remaining equally likely outcomes: BB, BG, GB.
4) Only BB satisfies 'both boys'.
5) Therefore probability is 1/3.Answer: P(both boys | at least one boy) = 1/3.
Answering 1/2 by assuming the other child is independent without conditioning.
How does answer change if condition is 'older child is a boy'?