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Question 270012
JEE Mathematics · Hard

Probability: JEE Main MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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JEE MainHardQuestion 270012

Question

If P(A) = 2/5, P(B) = 3/10, P(A ∩ B) = 1/5, then P(A' ∩ B') is:
  1. A
    1/2
    Correct
  2. B
    7/10
  3. C
    3/10
  4. D
    2/5

Correct answer

1/2

Explanation

P(A ∪ B) = P(A) + P(B) − P(A ∩ B) = 2/5 + 3/10 − 1/5 = 4/10 + 3/10 − 2/10 = 5/10 = 1/2. P(A' ∩ B') = P((A ∪ B)') = 1 − 1/2 = 1/2.

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