GATE AG 2021 • Q23 NAT • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Random variables

Question Statement:

The probabilities of A and B are given by P(A) = 0.35 and P(B) = 0.25, respectively. If A and B are mutually exclusive so that P(A∪B) = P(A) + P(B), then the value of P(A/A∪B) is ______. [round off to 3 decimal places]

Official Answer Key:

0.583 to 0.584

Step-by-Step Solution & Explanation

P(A∪B) = 0.35 + 0.25 = 0.60. Since A ⊂ (A∪B), A ∩ (A∪B) = A, so P(A|A∪B) = P(A)/P(A∪B) = 0.35/0.60 = 0.5833.

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