1. The problem statement, all variables and given/known data I have to prove that for any two events A and B P(A and B|A) [tex]\geq[/tex] P(A and B| A or B) 2. Relevant equations P(A and B) = P(A) . P(B|A) P(A|B) = (P(A) . P(B|A))/P(B) 3. The attempt at a solution I tried to simplify the left side with this reasoning P(A and B|A) = P(A) . P((B|A)|A) = P(A) . P(B|A) = P(A and B) My reasoning for going from step 1 to two is that condition A is already fulfilled, and asking for it a second time is needless. My friend however, disagrees with this. I am having problems with simplifying the right side because I don't know if there is a system of priorities in probability mathematics (e.g. "condition" has a priority over "and", "or" over "condition", ... Any help in the right direction would be greatly welcomed.