Question

if you are dealt 3 cards from a shuffled deck of 52 cards, find the probability of getting one queen and two kings
click the icon to view a description of a standard deck of playing cards.
the probability is
(round to six decimal places as needed.)

Explanation:

Step1: Calculate combination for one queen

The number of ways to choose 1 queen out of 4 is \(C(4,1)=\frac{4!}{1!(4 - 1)!}=\frac{4!}{1!3!}=4\)

Step2: Calculate combination for two kings

The number of ways to choose 2 kings out of 4 is \(C(4,2)=\frac{4!}{2!(4 - 2)!}=\frac{4\times3\times2!}{2!×2!}=6\)

Step3: Calculate total combination of 3 - card hands

The number of ways to choose 3 cards out of 52 is \(C(52,3)=\frac{52!}{3!(52 - 3)!}=\frac{52\times51\times50\times49!}{3!×49!}=22100\)

Step4: Calculate probability

The probability \(P=\frac{C(4,1)\times C(4,2)}{C(52,3)}=\frac{4\times6}{22100}=\frac{24}{22100}\approx0.001086\)

Answer:

\(0.001086\)