Question

1. Find the probabilities of Poker hands not covered in class. Recall in a Poker game, 5 cards are drawn uniformly at random from a deck of 52 cards. Each deck has 13 denominations ({A, 2, 3, . . . , 10, J Q, K)) and 4 suits (4,◇,0,6 ). In what follows consecutive denominations are But (J,Q,K, A, 21 is not considered consecutive. Find the probabilities of a. Straight Flush (5 cards of consecutive denomination, all of the same suit but not a royal flush, e.g. (2,3,4,5,6) of diamonds.) b. Full house (3 cards of one rank and two cards of another rank. e.g. 5,5, J,J,J, with no restriction on the suits). c. Flush (5 cards of the same suit, but not of consecutive denomination. e.g. 3,4, 9 ,J, Q, all of spades). d. Straight (5 cards of sequential rank, but not all of same suit excluding Royal Flush and Straight e. Three of a kind (Three cards of one denomination and two other denominations, e.g. 2,2,2, K,6, no f. Two pair (Two cards of one denomination, two cards of another denomination and another card of Flush. e.g. 3 of hearts,4 of spades,5 of spades,6 of diamonds,7 of diamonds ). restriction on suits). a third denomination. e.g. 3,3, J,J, K, no restriction on suits)

Answer 1