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 the 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:
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 the 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:
Option 1 -
Greater than
Option 2 -
Greater than but less than
Option 3 -
Exactly equal to
Option 4 -
Greater than but less than
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1 Answer
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Correct Option - 1
Detailed Solution:.(i)
.(ii)
.(iii)
Adding (i), (ii) and (iii) we get
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