Probability Calculation for Poker Hand with Four Cards of One Kind
Learn how to find the probability of getting a hand in poker that contains four cards of the same kind out of five. Understand the application of the product rule to calculate the chances of this specific poker hand occurrence.
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Presentation Transcript
Discrete Math: Example 5 of Finite Probability
Example 5 Find the probability that a hand of five cards in poker contains four cards of one kind.
Solution By the product rule, the number of hands of five cards with four cards of one kind is the product of the number of ways to pick one kind, the number of ways to pick the four of this kind out of the four in the deck of this kind, and the number of ways to pick the fifth card. This is C(13, 1)C(4, 4)C(48, 1). By Example 11 in Section 6.3 there are C(52, 5) different hands of five cards. Hence, the probability that a hand contains four cards of one kind is
References Discrete Mathematics and Its Applications, McGraw-Hill; 7th edition (June 26, 2006). Kenneth Rosen Discrete Mathematics An Open Introduction, 2nd edition. Oscar Levin A Short Course in Discrete Mathematics, 01 Dec 2004, Edward Bender & S. Gill Williamson
