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Let A, B, C be three events. If the prob...

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

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