Question

if you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are picture cards. click the icon to view a description of a standard deck of playing cards. the probability is \boxed{}. (round to six decimal places as needed.)

Explanation:

Step1: Determine number of picture cards

A standard deck has 12 picture cards (4 Jacks, 4 Queens, 4 Kings).

Step2: Calculate combinations for 4 picture cards

The number of ways to choose 4 picture cards from 12 is \( C(12, 4)=\frac{12!}{4!(12 - 4)!}=\frac{12\times11\times10\times9}{4\times3\times2\times1}=495\).

Step3: Calculate total combinations of 4 cards

The number of ways to choose 4 cards from 52 is \( C(52, 4)=\frac{52!}{4!(52 - 4)!}=\frac{52\times51\times50\times49}{4\times3\times2\times1}=270725\).

Step4: Compute probability

Probability \( P=\frac{C(12, 4)}{C(52, 4)}=\frac{495}{270725}\approx0.001828\).

Answer:

\(0.001828\)