Question: 1. Let A, B, C be events. If P(A|C) > P(B|C) and P(A|C') > P(B|C') either prove that P(A) > P(B) or give a counterexample

1. Let A, B, C be events. If P(A|C) > P(B|C) and P(A|C') > P(B|C') either prove that P(A) > P(B) or give a counterexample by defining an experiment, its sample space, and event A, B, C for which it is not true. Give an algebraic proof. A Venn Diagram is not sufficient.

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