SOLUTION: Suppose that you hold three aces and two different small cards in a game of draw poker. I you discard the two small cards, what are your chances of improving your hand on the draw?

Question 189438This question is from textbook
: Suppose that you hold three aces and two different small cards in a game of draw poker. I you discard the two small cards, what are your chances of improving your hand on the draw? The hand will be improved either by drawing another ace and any other card or by drawing a pair. (hint: Because this is a fair game and you do not know what cards are in the other players' hands, treat their cards as if they were part of the deck.) This question is from textbook

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
52-5=47cards that you can draw.
47C2=1081 possible different combinations of 2 card draws from 47 cards.
Ax=(1C1)(46C1)=1*46=46/1081 four aces
pp=(4C2)*10=6*10=60/1081 pair not containing an ace or the denomination of one of the cards you discarded.Full house.
dd=(3C2)*2=3*2=6/1081 pair containing the denomination of one of the cards you discarded. Full house.
46+60+6=110
110/1081 Chance of improvement.
.
Ed
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