calculating holdem probability - flush draw vs two-pair

[davidw]

It's been a while since I took probability... How do you combine the odds in this example:

I have two pair on the flop, my opponent is on a flush draw (9 outs, none of his flush outs completes my full house).

The probability of him hitting his flush by the river is Pflush = 1 - (36/45 * 35/44) =~ .36

The probability of me making a full house by the river is Pboat = 1 - (41/45 * 40/44) =~ .17


How do I find the probability of my opponent having the winning hand? I think works out like this but how do you expand this out to find the final probability?

P(makes flush on turn AND I don't make full house on river) OR P(makes flush on river AND I don't make full house on turn)

Thanks.