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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 pr
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Nov 13, 2021
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JackTerrance
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( ˉ A )+P( ˉ B )=2-2p+q Select the correct answer from above options
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Nov 13, 2021
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JackTerrance
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given that, p=P(A)+P(B)-P(A∩B) q=P(A)+P(B)-2⋅P(A∩B) p-q=P(A∩B) P( ˉ A )+P( ˉ 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 =RHS
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