Probability Proof: P(Ai)>0 for i=1-n, P(B)>0

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Easy16
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P(Ai)>0, for i=1,2,...n. P(B)>0. Show that if P(A1lB)<P(A1), then P(AilB)>P(Ai), for at least 1 value of i.
 

Discussion

If you assume Ai are disjoint and the all Ai's fill up the sample space, then it is easy.
Sum of P(Ai)=1 and Sum P(Ai|B)=1. You should be able to do the rest.
 

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