I came across this probability problem.
In a Texas Hold’em game, you are dealt 2 cards in your hands and the 3 flop cards are shown. You observe 4 diamonds out of the 5 cards. What are your chances of getting a flush?
Given that I see 4 diamonds already, isn't the probability just ${{13 - 4}\over{52 - 4}} = {3\over{16}}$? What am I missing?
Update: So in response to the comments, then the answer should simply be $1 - \left({{38}\over{47}}\right)\left({{37}\over{46}}\right) = {{378}\over{1081}}$?