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GATE DA 2024 Q7: Probability of two girls and one boy in three children

Question

The probability of a boy or a girl being born is 1/21/2. For a family having only three children, what is the probability of having two girls and one boy?

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Answer: A (official GATE 2024 final answer key)

Concept used: Binomial probability: (nk)pk(1−p)n−k\binom{n}{k} p^k (1-p)^{n-k}.

First step: The boy can be any one of the three children: (31)(12)3\binom{3}{1} \left(\tfrac{1}{2}\right)^3.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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