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Let A and B be events in a sample space (S,P) with P(B) not equal to zero. Suppose also that for all x in S, P(x) is not equal to zero.

In part (a) I proved that P(A|B) = 1 iff B is a subset of A.

I don't understand how to proof what is stated in the Title.

Thanks for the help in advance!

1 Answers 1

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Hint: Consider you can write $P(B) = P(B_1\cup B_2) = P(B_1)+P(B_2)$ with some disjunct $B_1, B_2$ and $P(B_2)=0$

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    Yes, this is just a hint how you can construct a counter example. You shoul choose $B=B_1\cup B_2$ with $P(B_1)\gt 0$ and some $B_2$ with $P(B_2)=0$ but $B_2\neq\emptyset$. Don't think to much about it .. you can even construct such an counter example on $S=\{0,1\}$ or sth like that2012-12-04