[DiceyPlay]

You added the probabilities of you getting it on the turn and then getting it on the river (given you didn't get it on the turn).

In reality you can get it on the turn or the river or both and to calculate it that way you would have to add these probabilities

p(get it on turn) * p(don't get it on river)
+
p(don't get it on turn) * p(get it on river)
+
p(get it on turn) * p(get it on river)

But that's the hard way. The easy way is to use the fact that the probability of you getting it + the probability of you not getting it is equal to 1.

So p(making fh or better) = 1 - p(not making fh or better)

And p(not making fh or better) is an easy calc.

p(not making fh or better) = 40/47 * 36/46 ~ .666

So p(making fh or better) ~ .334

-DP