Question

Let A, B, C be three events. If the probability of occuring 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 xạ, then prove that the probability that atleast one out of A,B,C
will occur is greater than 1/2.
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Answer 1

Answer:

Let,,be three events. If the probability of occurring exactly one event out ofandis, out ofandis, out ofandisand that of occurring three events simultaneously is, then prove that the probability that at least one out of,,will occur is greater than 1/2