Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In bridge, exactly 3 kings and exactly 3 queens
A)0.00097
B)0.00018
C)0.00337
D)0.00024

Question

Quizplus · Accepted Answer

The probability of getting exactly 3 kings and exactly 3 queens in a 13-card bridge hand can be calculated using combinations. There are 4 kings and 4 queens in a deck, so the ways to choose 3 kings out of 4 is $C(4,3)$, and the ways to choose 3 queens out of 4 is $C(4,3)$. The remaining 7 cards can be any of the 44 cards that are not kings or queens, so the ways to choose these 7 cards is $C(44,7)$. The total number of ways to choose any 13 cards out of 52 is $C(52,13)$. Therefore, the probability is $\frac{C(4,3) \times C(4,3) \times C(44,7)}{C(52,13)}$, which calculates to approximately 0.00097.

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