Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low.
-Two pair ( 2 cards of one value, 2 of another value)
A) $\frac { 20592 } { 433115 }$
B) $\frac { 22464 } { 433115 }$
C) $\frac { 5148 } { 433115 }$
D) $\frac { 3432 } { 433115 }$

Question

Quizplus · Accepted Answer

Two pair is a hand with two cards of one value and two cards of another value. There are 13 possible values for the two pairs, and for each value, there are 6 ways to choose the two cards of that value. There are 4 ways to choose the fifth card. So, the total number of two pair hands is 13 * 6 * 6 * 4 = 20592. The total number of possible five-card hands is 52 * 51 * 50 * 49 * 48 = 433115. So, the probability of two pair is 20592 / 433115 = 1/21.

Find the Probability of the Following Five-Card Poker Hands from a 52-Card