Question

Please explain your work. Thanks.

Compute the probability of each of the following poker hands occurring (poker hand = 5 cards dealt out of a regular 52-card deck, the order does not matter). For the following explanations, let the letters u, v, w, x, y, z indicate face values (i.e. ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king). Please note that aces can be either high (that is, they come after the king sequentially) or low (that is, they act like a “one”), but never both at the same time.

a. Royal flush (10, jack, queen, king, ace; all of the same suit)

b. Straight flush (not royal) (five sequential cards, all of the same suit)

c. Four of a kind (x, x, x, x, y)

d. Flush (not straight or royal) (five cards, not all sequential, of the same suit)

e. Straight (not royal or flush) (five sequential cards, not all of the same suit)

f. Full house (x, x, x, y, y) g. Three of a kind (x, x, x, y, z)

h. Two pairs (x, x, y, y, z) i. At least 4 face cards (face cards are jacks, queens, and kings)

j. No more than one ace

Answer 1