# Can P[A | (A intersection B) ] be written as below? (Probability Ques)

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## 1 Replies - 3393 Views - Last Post: 11 February 2013 - 02:26 PM

### #1 deprosun

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# Can P[A | (A intersection B) ] be written as below? (Probability Ques)

Posted 10 February 2013 - 03:50 PM

Can P[A | ( A intersection B )] be written as:
P(A intersection B )/ P(A intersection B )?

Given that A, B, and C are three sets where,
P( B )>0, P(A')>0, and P(A intersection B )>0.

By Conditional probablity laws:
P( A|B ) = P( A intersection B )/ P( B )

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## Replies To: Can P[A | (A intersection B) ] be written as below? (Probability Ques)

### #2 mojo666

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## Re: Can P[A | (A intersection B) ] be written as below? (Probability Ques)

Posted 11 February 2013 - 02:26 PM

Yes, fairly trivially. Just take the law P(C|D) = P(C intersect D)/ P(D) and substitute C with A and D with (A intersect B ). Simplify the result.

This post has been edited by mojo666: 11 February 2013 - 02:26 PM