What is the probability of drawing Two Pair in a poker hand from a 52-card deck?
I have my answer, but for some reason it is exactly double the correct answer.
I haven't been able to figure out why. Here's my solution:
First you draw an arbitrary card.
To pair it, the probability is 3/51.
Next, you want to draw a different card.
There are 48 such cards out of 50, so the probability is 48/50.
You seek its pair, which has probability 3/49.
Your final card must be different from both the originals
(otherwise we'd have a full house), so it has probability 44/48.
That yields approx. 0.00316.
There are precisely 5!/(2!*2!*1!) orderings of two pair hands = 30.
Thus, 30 * 0.00316 = 0.09507.
But the correct answer is half that.