Given P(A|B∪C)≥min(P(A|B),P(A|C)), prove or disprove the statement. My intuition said that the statement should be correct, however I can't think of a mathematical way of proving this statement. Any suggestion is highly appreciated
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Then $\Pr(A|B)=\Pr(A|C)=0.6/0.8 = 0.75$
but $\Pr(A|B \cup C) = 0.6/1.0 = 0.6$.
So the statement is not always true.