Question

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

Answer 1

If \(A\) and \(B\) are independent, then \(\mathbb{P}(A|B)=\dfrac{\mathbb{P}(A\cap B)}{\mathbb{P}(B)}=\dfrac{\mathbb{P}(A)\mathbb{P}(B)}{\mathbb{P}(B)}=\mathbb{P}(A)\). Similarly, \(\mathbb{P}(B|A)=\mathbb{P}(B)\).