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Let A, B and 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 x^2, then prove that the probability that atleast one out of A, B and C will occut is greater than $\frac{1}{2}$

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Solution

Atleast one out of A B and C will occur is greater than $\frac{1}{2}$

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Q. For three events

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C, P (

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B

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exactly one of the vents

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all the three events occur simultaneously

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0 < p < \frac{1}{2}

.
Then the probability of atleast one of the three events

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Q. For three events

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= \frac{1}{16}

. Then the probability that at least one of the events occurs, is.

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the probability that exactly one of

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Q. For three events A, B and C, if P (exactly one of A or B occurs) = P(exactly one of B or C occurs) = P (exactly one of C or A occurs)

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then the probability that atleast one of the events occurs is ?

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(Exactly one of

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B

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the probability that at least one of the events ocurs is

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