Question

Pr(A|B)=Pr(B|A)

true or false?

Answer 1

This statement will only be true in the event that P(A) = P(B)

Since by Bayee's theorem we have that

P(A/B) = =P(B/A)

if P(A) = P(B)

However, like justin rising points out we have to consider the event that A and B are mutually exclusive that is the event that A B = 0.

Assuming this is the case, and that the events A and B both have probability measure larger than zero.

P(A/B) = = = =

So summing it up we have

P(A) = P(B) or P(A B) = 0

=> P(A/B) = P(B/A).