Question

In Texas Hold’em, each player is dealt two cards from the deck. Obviously, this is done without replacement, so you cannot use the binomial distribution. You can use the hypergeometric distribution or reason from first principles.

a) What is the probability of being dealt a pair? Express it as an exact fraction and an approximate percentage.

b) If you are dealt two unpaired cards, say the ace of clubs and the 8 of diamonds, what is the chance of getting a pair or better on the flop? The flop is three cards dealt all at once, and we want to know the chance that the flop will contain at least one ace or at least one 8.

Answer 1

a) the probability of being dealt a pair = 4C2 * 13 / 52C2 = 0.05882353

How., so we have 4 cards of same denomination from which we can choose 2 cards and such 13 denominations are there hence 13 * 4C2 and we have total 52 cards from which we will get 2 hence total possibilities of getting 2 cards from a deck is 52C2

b) dealt two unpaired cards, say the ace of clubs and the 8 of diamonds, what is the chance of getting a pair or better on the flop

So we need to get either a queen or an 8 and we have 50 cards left from which 3 cards will be given

Hence total occurrences are 50C3

but the chances we are looking for are any 1 from the 6 cards (3 aces and 3 diamonds to be given) and then rest of the 49 cards you will be dealt with 2 i.e. 6C1 * 49C2

Hence the probability = 6C1 * 49C2/50C3 =0.36

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!