Sex of the other baby when one is a girl

Question

A woman has two babies, and you learn that at least one of them is a girl. Assuming each baby is independently a boy or girl with equal probability, what is the chance that the other baby is a boy?

Short answer

$2/3$ . The equally likely families are BB, BG, GB, GG; knowing at least one girl leaves BG, GB and GG, and two of those three contain a boy. (If instead you were told a particular baby is a girl, the answer would be $\tfrac12$ .)

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q3.14, p.82; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating
Sample Spaces, Events, and the Probability Axioms

Start with a free lesson: Probability Fundamentals is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free