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NDA 1 2024 Maths, question 111

Topic: Probability

Passage · Q111 to Q112

Let AA and BB be two events such that P(A∪B)≥0.75P(A\cup B)\ge 0.75 and 0.125≤P(A∩B)≤0.3750.125\le P(A\cap B)\le 0.375.

Q111

What is the minimum value of P(A)+P(B)P(A)+P(B) ?

  1. (a) 0.6250.625
  2. (b) 0.7500.750
  3. (c) 0.8250.825
  4. (d) 0.8750.875Correct answer

Solution.

Answer: (d) 0.8750.875

  1. Use P(A) + P(B) = P(A ∪ B) + P(A ∩ B).
  2. The smallest permitted values are 0.75 and 0.125, giving 0.875.
  3. They are jointly attainable, for example with each exclusive part 0.3125.