Question

in 5 - card poker, find the probability of being dealt the following hand. refer to the table.
note that a standard deck of playing cards has 52 cards - 4 suits (clubs,
diamonds, hearts, spades), where each suit has 13 cards (ace, 2, 3, 4, 5, 6, 7, 8, 9,
10, jack, queen, king).
a clubs flush (not a royal flush or a straight flush)
the probability of being dealt a clubs flush is
(type an integer or decimal rounded to eight decimal places as needed.)

Explanation:

Step1: Determine the number of clubs flush hands

A clubs flush (not royal or straight) is calculated as the total number of 5 - card clubs hands minus royal flush (1) and straight flush (9).
The number of 5 - card clubs hands is \(C(13,5)=\frac{13!}{5!(13 - 5)!}=\frac{13\times12\times11\times10\times9}{5\times4\times3\times2\times1}=1287\)
Number of clubs flush (not royal or straight) \(=1287-(1 + 9)=1277\)

Step2: Calculate the probability

The total number of 5 - card hands from a 52 - card deck is \(C(52,5)=\frac{52!}{5!(52 - 5)!}=2598960\)
Probability \(P=\frac{1277}{2598960}\)

Step3: Compute the decimal value

\(P=\frac{1277}{2598960}\approx0.00049135\)

Answer:

\(0.00049135\)