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# Basic Probability Watch

1. Question is

Prove that P(A|B n C) = P(A|C)P(B|A n C)/P(B|C)

I started off with P(A n B) = P(A|B)P(B) = P(B|A)P(A) and let B n C become one event D (Probably completely unnecessary!) to give me

P(A|D) = P(A|B n C) = P(A n(B n C))/P(B n C)

Not really sure how to continue from here, if anyone could give me a hint or a link to a proof elsewhere it would be much appreciated!
2. (Original post by Tom722)
Question is

Prove that P(A|B n C) = P(A|C)P(B|A n C)/P(B|C)

I started off with P(A n B) = P(A|B)P(B) = P(B|A)P(A) and let B n C become one event D (Probably completely unnecessary!) to give me

P(A|D) = P(A|B n C) = P(A n(B n C))/P(B n C)

Not really sure how to continue from here, if anyone could give me a hint or a link to a proof elsewhere it would be much appreciated!

Similarly

Rearrange for and substitute into and it should fall out nicely
3. Eureka! Thanks a lot!

(Apparently I've recently given you a thumbs up, hope you aren't too distraught I can't give you another!)

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