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This question is commonly asked for Data Scientist candidates at Amazon during technical interviews.

Determine Probability of Both Children Being Boys

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of conditional probability, probabilistic reasoning, and the role of underlying assumptions when enumerating sample spaces, which are core competencies for data scientists.

Amazon

Jul 12, 2025, 6:59 PM

Data Scientist

Technical Screen

Statistics & Math

Probability: Two-Child Family

Context

You are considering families with exactly two children. A statement is revealed: "At least one of the children is a boy." Determine the probability that both children are boys. Clearly state any assumptions you make.

Question

What is P(both children are boys | at least one child is a boy)?

Hint:

Enumerate the equally likely ordered outcomes: BB, BG, GB, GG.
Condition on the information "at least one is a boy."

Solution

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