Question

A deck of 52 playing cards, containing all 4 aces, is randomly divided into 4 piles of 13 cards each. Define events $E_{1}, E_{2}, E_{3}$, and $E_{4}$ as follows: $E_{1}=\{$ the first pile has exactly 1 ace $\}$, $E_{2}=\{$ the second pile has exactly 1 ace $\}$, $E_{3}=\{$ the third pile has exactly 1 ace $\}$, $E_{4}=\{$ the fourth pile has exactly 1 ace $\}$ Use Exercise 23 to find $P\left(E_{1} E_{2} E_{3} E_{4}\right)$, the probability that each pile has an ace.

          A deck of 52 playing cards, containing all 4 aces, is randomly divided into 4 piles of 13 cards each. Define events $E_{1}, E_{2}, E_{3}$, and $E_{4}$ as follows:
$E_{1}=\{$ the first pile has exactly 1 ace $\}$, $E_{2}=\{$ the second pile has exactly 1 ace $\}$, $E_{3}=\{$ the third pile has exactly 1 ace $\}$, $E_{4}=\{$ the fourth pile has exactly 1 ace $\}$
Use Exercise 23 to find $P\left(E_{1} E_{2} E_{3} E_{4}\right)$, the probability that each pile has an ace.

Added by Thomas P.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Md.Daniyal Arshad

12/13/2021

Step 1

There are 4 aces that need to be distributed into 4 piles, which can be done in 4! ways. ** Show more…

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A deck of 52 playing cards, containing all 4 aces, is randomly divided into 4 piles of 13 cards each. Define events $E_{1}, E_{2}, E_{3}$, and $E_{4}$ as follows: $E_{1}=\{$ the first pile has exactly 1 ace $\}$, $E_{2}=\{$ the second pile has exactly 1 ace $\}$, $E_{3}=\{$ the third pile has exactly 1 ace $\}$, $E_{4}=\{$ the fourth pile has exactly 1 ace $\}$ Use Exercise 23 to find $P\left(E_{1} E_{2} E_{3} E_{4}\right)$, the probability that each pile has an ace.