The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?
P(B|A) = y
P(A|B) = y
P(B|A) = x
P(A and B) = x + y

P(A and B) = x

P(A) y

Question

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?
P(B|A) = y
P(A|B) = y
P(B|A) = x
P(A and B) = x + y

P(A and B)	=	x

P(A)		y

ciarán95 · Answer

P(B|A) is the probability of B occurring, given that A has already occurred. But, if A and B are independent of each other, then the probability of either happening should not depend on whether the other event has taken place already. So as P(B) = y, P(B|A) = y is the true condition.