Suppose you repeatedly play hands of Texas HoldSolutionAnswe

Suppose you repeatedly play hands of Texas Hold

Solution

Answer

The probability mass function of a random variable X with hypergeometric distribution is given by the following recurrence relation:

(k+1)(N - K -(n-k-1)) P(X = k+1) = (K-k)(n-k) P(X = k) with

P(X = 0) = (N-k n)/ (N n)

In Hold\'em Poker players make the best hand they can combining the two cards in their hands with the five cards(community cards) eventually turned upon the table. The deck has 52 and there are 13 of each suit.

There are four clubs showing , so there are 9 still unseen. There are 5 cards showing,so there are 52-5 = 47 still unseen.

The probability that one of the next two cards turned is a club can be calculated using hypergeometric with k = 1, n=2, K =9 and N=47(about 31.6%).

The probability that both of the next cards turned are clubs can be calculated using hypergeometric with k = 2, n =2, K=9 and N=47(about 3.3%).

The probability that neither of the next two cards turned are clbs can be calculated using hypergeometric with k=0, n=2,K=9 and N=47(about 65.0%).