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If A and B are any two events such that `P(A) + P(B) - P(A a n d B) = P(A)`? then
(A) `P(B | A) = 1`
(B) `P(A | B) = 1`
(C) `P(B | A) = 0`
(D) `P(A | B) = 0`

Text Solution

Verified by Experts

`P(A)+P(B)−P(A and B)=P(A)`
⇒`P(A)+P(B)−P(AnnB)=P(A)`
⇒`P(B)−P(AnnB)=0`
⇒`P(AnnB)=P(B)`
∴`P(A/B)= (P(AnnB))/(P(B))`
= `P(A/B)=(P(B))/(P(B)) =1`
Thus, the correct answer is B.
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