Overview
The boy-or-girl paradox shows how a seemingly innocent phrase — 'at least one' — quietly reshapes a probability. The wording of a condition is everything.
How to solve The Boy or Girl Paradox
- List the equally likely ordered outcomes for two children: BB, BG, GB, GG.
- 'At least one boy' removes only GG, leaving three equally likely cases.
- Both-boys (BB) is just one of those three, so the probability is ⅓.
The key insight
Conditioning on 'at least one boy' keeps the two mixed orders BG and GB, which together outweigh BB two-to-one. Order matters when you count the sample space.
Variations & echoes
- Change the clue to 'the older is a boy' and the answer jumps to ½.
- The subtle 'Tuesday boy' variant shifts the probability again, revealing how fragile such conditionals are.
Frequently asked questions
Why isn't it ½?
Because 'at least one boy' allows BB, BG and GB — three cases — and only one has two boys. Naming a specific child (e.g. the older) would instead give ½.