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NDA 2024 · PYQ · Probability · medium

Let A and B be two events such that P(A∪B) ≥ 0.75 and 0.125 ≤ P(A∩B) ≤ 0.375. What is the maximum value of P(A) + P(B)?

Answer

The correct answer is C: 1.375. P(A) + P(B) = P(A∪B) + P(A∩B). To maximize, take maximum P(A∪B) = 1 and maximum P(A∩B) = 0.375.

  1. A.0.75
  2. B.1.125
  3. C.1.375✓ Correct
  4. D.1.625

Explanation

P(A) + P(B) = P(A∪B) + P(A∩B). To maximize, take maximum P(A∪B) = 1 and maximum P(A∩B) = 0.375. So maximum P(A)+P(B) = 1 + 0.375 = 1.375.
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