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Probability question

2021 · 20 Jul · Shift 2 · Q31
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  5. /2021 · 20 Jul · Shift 2 · Q31

Probability question

2021 · 20 Jul · Shift 2 · Q31

JEE MainMathematicsProbabilityMCQ+4 / −1
Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 −-− k), the probability that exactly one of B and C occurs is (1 −-− 2k), the probability that exactly one of C and A occurs is (1 −-− k) and the probability of all A, B and C occur simultaneously is k2, where 0 < k < 1. Then the probability that at least one of A, B and C occur is :
  1. A
    greater than 18{1 \over 8}81​ but less than 14{1 \over 4}41​
  2. B
    greater than 12{1 \over 2}21​
  3. C
    greater than 14{1 \over 4}41​ but less than 12{1 \over 2}21​
  4. D
    exactly equal to 12{1 \over 2}21​
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