(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider two events A and B such that p(A) = r and p(B) = s with r,s >0 and r + s > 1.

Show that

P(A|B) >or= 1- ( (1-r)/s)

2. Relevant equations

3. The attempt at a solution

By definition

P(A|B) = P(A & B) / P(B)

We know P(B) = s, so we need an inequality

p(A & B) >= something ...... (*)

P(A & B) = P(A) + P(B) - P(A or B)

P(A) and P(B) are given, and we know P(A or B) <= 1

Now (1-r) = p(A'),

So how to I show that p(A & B) is > than p(A'),

regards

Brendan

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