Boy ratio when families stop at the first son
Question
In some society each couple keeps having children until a son is born, and then stops. Every birth is independently a boy or a girl with probability each. As the population grows over time, what fraction of the children born are boys?
Short answer
50%. The stopping rule changes how many children each family has, but every individual birth is still an independent fair coin flip. Hence the expected numbers of boys and girls born are always equal, and the proportion of boys tends to one half.
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
See the hint and the full worked solution in the question bank (free account).
Open the worked solutionLessons behind this question
- Independence
- Sample Spaces, Events, and the Probability Axioms
- Conditional Probability, Total Probability, and Bayes' Rule
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