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2023 PEA Q18

Choose n∈{1,2,…,6}n\in\{1,2,\dots,6\} uniformly, then choose m∈{1,…,n}m\in\{1,\dots,n\} uniformly. Probability that m=5m=5?

The available source text does not include a full option block for this item, so the question is marked needsReview.
Reveal answer and solution

Answer

B

Solution

  1. 1

    m=5m=5 requires n≥5n\ge 5. So

  2. 2
    P(m=5)=∑n=5616⋅1n=16(15+16)=16⋅1130=11180. P(m=5)=\sum_{n=5}^{6}\frac{1}{6}\cdot\frac{1}{n}=\frac{1}{6}\Bigl(\frac{1}{5}+\frac{1}{6}\Bigr)=\frac{1}{6}\cdot\frac{11}{30}=\frac{11}{180}.

Answer structure / marking notes

Needs review: source TeX does not provide a full four-option MCQ block.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2023/ISI_MSQE_PEA_2023_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.