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2022 PEA Q28

A family has two children. Find the probability that both are boys given that at least one is a boy.

Reveal answer and solution

Answer

C

Solution

  1. 1

    Sample space: {BB,BG,GB,GG}\{BB, BG, GB, GG\}, each with probability 1/41/4. Condition on {\{at least one

  2. 2

    boy}={BB,BG,GB}\} = \{BB, BG, GB\}, of size 3/43/4. Among these, only BBBB has both boys:

  3. 3
    P(BB∣at least one boy)=1/43/4=13. P(BB \mid \text{at least one boy}) = \frac{1/4}{3/4} = \frac{1}{3}.

Answer structure / marking notes

At least one boy'' is not the same as the first is a boy''; the latter would give 1/21/2.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.