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2022 PEA Q29

Box 1 contains {1\{1 black, 11 white}\}; Box 2 contains {1\{1 black, 22 white}\}. Select a box at random and then a ball at random. Probability that the drawn ball is black?

Reveal answer and solution

Answer

A

Solution

  1. 1
    P(B)=12⋅12+12⋅13=14+16=3+212=512. P(B) = \frac{1}{2}\cdot\frac{1}{2} + \frac{1}{2}\cdot\frac{1}{3} = \frac{1}{4} + \frac{1}{6} = \frac{3 + 2}{12} = \frac{5}{12}.

Answer structure / marking notes

Apply the law of total probability with equal prior weight on each box.

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.