Let `A` ,`B` ,`C` be three events. If the probability of occurring exactly one event out of `A` and `B` is `1-x `, out of `B` and `C` is `1-2x `, out of `C` and `A` is `1-x ` and that of occurring three events simultaneously is `x^2` , then prove that the probability that at least one out of `A`, `B`, `C` will occur is greater than 1/2 .

Explanation

`= P(A⋃B) – P(A⋂B)`



`= P(A) + P(B) – 2P(A⋂B)`



`So P(A) + P(B) – 2P(A⋂B) = 1-a ..(i)`



`Similarly P(B) + P(C) – 2P(B⋂C) = 1-2a ..(ii)`



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