Given events A, B, C in a probability space, I want to prove:
min(P(C|A), P(C|B))/2 <= P(C|(A or B))
However it doesn't seem to be working out for me, although it makes sense intuitively. Any hints?
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Here it is: Suppose for instance that . Then .
In addition, .
These two inequalities should suffice to prove your inequality.
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