conditional probability proof

vortex42 · #1 $Old$ 09-05-2008, 06:24 PM

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?

Laurent · #2 $Old$ 09-06-2008, 04:12 AM

Here it is: Suppose for instance that $P(A)\geq P(B)$ . Then $P(A\cup B)\leq 2P(A)$ .
In addition, $P(C\cap(A\cup B))\geq P(C\cap A)$ .
These two inequalities should suffice to prove your inequality.

Laurent.