Easy · Probability & Combinatorics · Multiple choice · ~3 min · #4

At Least One Boy

Real interview · D. E. Shaw

A family has two children. You learn that at least one of them is a boy. Assuming each child is independently a boy or a girl with probability $\tfrac12$ , what is the probability that both children are boys?

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Reported in interviews

D. E. ShawGlassdoor interview question

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

Conditional probabilityRestricting the sample space

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