Even if you don't know how to play, the math question is combinatorial.

If you start with 5 cards, and 3 of them are of 1 suit (say clubs), what are the odds of drawing 2 more clubs to complete a flush?. There are 8 cards to come.

Notation: (4,1) means "4 choose 1"

My guess:
(10,2)*(37,6)/(47,8) ~= 33.3%
But that only counts the chances of drawing EXACTLY 2 clubs.

So we need to take the sum of the odds of drawing 2 through 8 clubs.
SUM{n=2..8}{(10,n)*(37,8-n)/(47,8)} ~= 55.0%

Does this look right?