Calculate Probability of Both Children Being Boys

Q: Calculate Probability of Both Children Being Boys

This question evaluates understanding of conditional probability and sample-space reasoning, assessing probabilistic and statistical thinking relevant to data analysis at a conceptual understanding level.

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Question

Conditional Probability: The Two-Child Problem

Context and Assumptions

Each child is independently a boy or a girl with probability 1/2.
Birth order matters (older, younger), and twins/other complexities are ignored.
The statement "at least one is a boy" provides only that constraint and does not bias which families are reported beyond ruling out two-girl families.

Question

A family has two children. You learn that at least one of them is a boy. What is the probability that both children are boys? Explain your reasoning.

Hint

List equally likely ordered pairs: BB, BG, GB, GG; remove combinations inconsistent with the condition.

Calculate Probability of Both Children Being Boys

Conditional Probability: The Two-Child Problem

Context and Assumptions

Question

Hint

Solution

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