(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Problem with a proof in probability

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