Allied & ICAR Exam Bank • ALLIED_2356 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

Bag I contains 3 red and 4 black balls. Bag II contains 5 red and 3 black balls. A ball is drawn at random from one of the bags and is found to be red. What is the probability that it was drawn from Bag I?

Options:

  • (A) 24/59
  • (B) 35/59
  • (C) 12/29
  • (D) 15/29

Answer Key:

A

Step-by-Step Solution & Explanation

$P(B_1) = P(B_2) = 1/2$. $P(R|B_1) = 3/7$, $P(R|B_2) = 5/8$. Total $P(R) = (1/2)(3/7 + 5/8) = (1/2)(59/56) = 59/112$. $P(B_1|R) = (3/14) / (59/112) = (3/14) \times (112/59) = 24/59$.
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