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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-x ,` out of `B and C` is `1-2x ,` out of `C and A` is `1-x ,` and that of occuring three events simultaneously is `x^2` , then prove that the probability that atleast one out of A, B, C will occur is greater than 1/2 .

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