Answer to Question #316155 in Statistics and Probability for Aswani

Question

A random 5-card poker hand is dealt from a standard deck of cards. Find the probability (in terms of binomial coefficients) of getting a flush (all 5 cards being of the same suit: do not count a royal flush, which is a flush with an ace, king, queen, jack and 10).

Answer 1

We can use 8 cards. (2,3,4,5,6,7,8,9)

At the first time we can get any suit. So Probability is 4$\times$ 8/52=0.62

Probability of second card is 7/51

Probability of third card is 6/50

Probability of fourth card is 5/49

Probability of 5 th card is 4/48

So $P=0.62\times 7/51\times 6/50\times 5/49\times4/48=0.000087$