I don't know why I am having such trouble with this. I've tried using De Morgan but haven't made much progress yet.
Prove if $a>0, b>0$, $P(X\cdot Y\le b)\ge P(X\le b/a)-P(Y>a)$, where $X,Y$ random variables?
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0Try drawing the regions in the x-y plane corresponding to each event. – 2011-11-16
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0Nevermind, did it via De Morgan. You are welcome to post another technique though. – 2011-11-16