Thank you for your help Question 4)Intermediate The \"flop\" of a texas hold\'em

Question

Thank you for your help

Question 4)Intermediate The "flop" of a texas hold'em game consists of drawing at random two cards of a standard deck of 52, Ordering irrelevant). a) How many distinct hands can you have in the "flop" of a texas hold'em game? b) What is the chance of you drawing the ace and the king of spades? c) What is the chance you will draw an ace and a king of the same suit? i A standard deck has cards going from A, 2, 3, 10, J, Q,K for each one of the four suits namely hearts, clubs, diamonds, and spades.

Explanation / Answer

Drawing two cards from a deck of 52 cards can be done in 52C2 ways i.e. n(S) = 1326

(A) There are total 1326 hands possible

(B)

Selecting the ace and the king of spades = 4C1 + 1 = 5 ways

Hence Probability = 5/1326

(C)

Selecting an ace and a king of the same suit = 4C1 = ways

hence Probability = 4/1326

(D)

Selecting two cards of spades = 13C2 = 78 ways

hence Probability = 78/1326

(E)

Selecting two cards of the same suit = 4C1 * 13C2 = 312

hence Probability = 312/1326

(F)

Selecting an ace and a king of the same suit = 4C1 = 4 ways

Selecting two cards of spades = 13C2 = 78

Hence Probability = (4+78)/1326 = 82/1326

(G)

Selecting a pair = 13C1 * 4C2 = 13 * 6 = 78

hence Probability = 78/1326

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