You are playing a poker game. You have 55 and the board reads 358 giving you 3 of a kind. There are two more cards to come. What's the probability you make a full house or better?
Here's my answer. You can only make a fullhouse or 4 of a kind. So on the first of the two cards to come, you can hit 7 out of 47 cards (3,5,or8). If you miss on the first card, you can hit 10 out of 46 cards. It's 10 because you can not only hit a 3, 5, 8 but also make a fullhouse by getting a pair in the last two cards. So, 1 - (prob(missing both cards)) = 1-(40/47 * (36/46)
But it should also add up to the probability of hitting on the 1st card + probability of hitting on the second card - the probability of hitting on both 1st and second card. So, 7/46 + 10/46 - 6/46. But my two answers don't tie. What am I doing wrong?