Question

if you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are clubs. 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 the number of ways to choose 4 club cards

There are 13 club cards in a deck. The number of ways to choose 4 club cards is given by the combination formula \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 13\) and \(r=4\).

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Step2: Calculate the number of ways to choose 4 cards from 52 cards

Using the combination formula with \(n = 52\) and \(r = 4\)

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Step3: Calculate the probability

The probability \(P\) that all 4 cards are clubs is the ratio of the number of ways to choose 4 club cards to the number of ways to choose 4 cards from 52 cards.

$$P=\frac{C(13,4)}{C(52,4)}=\frac{715}{270725}\approx0.002641$$

Answer:

\(0.002641\)