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NDA 2019 Maths · Mathematics · Probability · medium

Events A and B are independent with P(A)=1/3 and P(B)=1/4. The probability that neither of them occurs is

Single correct option

Events AA and BB are independent with P(A)=13P(A)=\frac13 and P(B)=14P(B)=\frac14. The probability that neither of them occurs is
  1. A. 512\frac5{12}
  2. B. 112\frac1{12}
  3. C. 12\frac12
  4. D. 712\frac7{12}
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Answer: (C) 12\frac12

For independent events the complements are also independent, so P(Aˉ∩Bˉ)=23⋅34=12P(\bar A\cap\bar B)=\frac23\cdot\frac34=\frac12. Alternatively P(A∪B)=13+14−112=12P(A\cup B)=\frac13+\frac14-\frac1{12}=\frac12, and the complement is again 12\frac12. The value 712\frac7{12} is P(A)+P(B)P(A)+P(B), which ignores the overlap.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake