Poker flush draw possibilities

[morrowcosom]

I am the only one drawing from the deck. I come out with two cards of matching suit. The flop them comes down with two cards matching my suit, therefore giving me a flush draw. What is the probability of getting a flush?

Here is my go at it:
(I am going by helping cards/unseen cards)

I already have 4 cards of the flush, so there are only 9 cards left out of the original 13 that help. I have seen 5 out of 52 cards so far, so 47 remain


On the turn: 9/47= 19.15% On the river: 9/46= 19.57%

So by adding these two together, I get a 38.72% of getting a flush by the river card, If I get a flush draw on the flop.

This seems correct, but if not, what is the error of my ways?

Thanks

 

[Valkarie]

for your help! Your calculation is correct. You have 4 cards towards the flush already, so you need one more of that suit to make a flush. There are 9 cards remaining in the deck that will give you that flush, out of 47 unseen cards (52 cards total - 5 cards you've seen). This means there is a 9/47 or 19.15% chance of making the flush on the turn and a 9/46 or 19.57% chance of making the flush on the river. When added together, this gives a 38.72% chance of making the flush by the river card.