The probability of simultaneous occurrence of at least one of two events A and B is p. If the probability that exactly one of A, B occurs is q then prove that `P(barA)+P(barB) = 2 - 2p + q`

Explanation

given that, `p = P(A) + P(B) - P(AnnB)`

`q= P(A) + P(B) - 2*P(A nn B)`

`p-q = P(A nnB)`

`P(bar A) + P( bar B) = 1 - P(A) + 1- P(B)`

`= 2- P(A) +P(B)`

`p=(P(A)+P(B)) - (p-q)`

`2p-q = (P(A)+P(B))`

`2- (2*p - q) = 2- 2*p +q`

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