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Topic: a puzzling conditional probability
Replies: 6   Last Post: Aug 23, 2012 4:21 AM

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Posts: 36
Registered: 10/17/07
a puzzling conditional probability
Posted: Aug 9, 2012 6:47 AM
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Given that:

P(A|B) = P(notA | notB) = 0.95
and B = 0.05

My goal is to calculate the conditional probability: P(notB|A). But how?

I have tried the following to get to the answer... but got stuck at some point, while trying to solve one of the subproblems. Please see below for the details:

It is known that: P(notB|A) = P(notB AND A) / P(A)

So, I would need to find P(A), but how? I thought one way to find P(A) would be:
P(A) = P(A AND B) AND P(A AND notB)

P(A AND B) is easy to calculate, i.e. P(A|B) x P(B) => 0.95 x 0.05 => 0.0475.
but how does one calculate the P(A AND notB) ???

Many thanks for help.

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