Math problem

[Endlestorm]

This is something that I have been thinking about for a while, but not enough to get too involved with the math. It stems from my dilemma with raising medium pocket pairs preflop.

You are in late position and make it 4x to go with 99. Button calls making it heads up. Flop comes something like Q82r giving you second pair. You assume that button would CALL with any pocket pair (say JJ or below), additionally AK,AQ,AJ,KQs,JTs.

What are the chances that he hit a set or top pair? How often can you expect to get played with if you fire on the flop? If you do get played with, are you way behind?

Thoughts?