Medium · Probability & Combinatorics · Multiple choice · ~7 min · #108

One of Them Is Named William

Real interview · D. E. Shaw

A family has two children, each independently a boy or girl with equal probability. You learn that at least one is a boy named William. Each boy is independently named William with a small probability $\varepsilon$ , and girls never are.

As $\varepsilon \to 0$ , 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
Asked as a harder follow-up. We state the naming assumption explicitly.

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 probabilityHow information is revealed

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