Under what conditions does P(B|A)=P(A|B)

Question

This is finite math. She said it’s a word answer. 

Answer 1

P(B l A) = P(A and B) / P(A)

 

P(A l B) = P(A and B) / P(B)

 

If P(B l A) = P(A l B), then P(A) = P(B).

Answer 2

this condition holds if P(A) = P(B)

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

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

the numerators are the same for both so the part that you need to be equal is P(A) = P(B) in order for this to be true