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For the three events `A`, `B` and `C`, `P`(exactly one of the events A or B occurs) `= P`(exactly one of the events B or C occurs) `=P`(exactly one of

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For the three events A, B and C, P(exactly one of the events A or B occurs) =P(exactly one of the events B or C occurs) =P(exactly one of the events C or A occurs)=p and P(all the three events occur simultaneously) =p2, where 0<p< 1 2 . Then, find the probability of occurrence of at least one of the events A, B and C. Select the correct answer from above options

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P(exactly one of the events A or B)=P{(A∩ ˉ B )∪( ˉ A ∩B)} p=P(A)+P(B)-P(A∩B) p=P(A)+P(C)-P(A∩C) p=P(B)+P(C)-P(B∩C) p2=P(A∩B∩C) P(A∪B∪C)=P(A)+P(B)+P(C)-P(A∩B)-P(B∩C)-P(A∩C)+P(A∩B∩C) P ( A ∪ B ∪ C ) = P ( A ) + P ( B ) + P ( C ) − P ( A ∩ B ) − P ( B ∩ C ) − P ( A ∩ C ) + P ( A ∩ B ∩ C ) = 3p 2 +p2 = 3p+2p2 2 .

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