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NDA 2 2025 Maths, question 119

Topic: Probability

Q119

If P(A)=1/3P(A)=1/3, P(B)=1/2P(B)=1/2 and P(A∩B)=1/4P(A\cap B)=1/4, then what is the value of P(A‾∪B‾)P(\overline{A}\cup \overline{B})?

  1. (a) 7/127/12
  2. (b) 2/32/3
  3. (c) 3/43/4Correct answer
  4. (d) 11/1211/12

Solution.

Answer: (c) 3/43/4

  1. The bars over A and B are essential.
  2. By De Morgan’s law, Aᶜ∪Bᶜ=(A∩B)ᶜ.
  3. Therefore P(Aᶜ∪Bᶜ)=1−1/4=3/4.
  4. The value 7/12 would instead be P(A∪B).