Question

A deck of 52 cards contains four aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all four aces will be received by the same player?

Answer 1

Answer:

The probability that all four aces will be received by the same player is approximately 0.01.

Step-by-step explanation:

Of the 52 cards the four  aces can be selected in $52\choose4$ ways.

If any one of the players receives all the four aces then that player can be selected in $4\choose1$ ways.

Now for the selected player to receive all the four aces, the four ace cards must be placed among the 13 cards the player receives. This can be done in $13\choose4$ ways.

Then the total number of ways such that all the four aces is received by one player is $4$ $13\choose4$.

Then the probability that all four aces will be received by the same player is:

$4\times\frac{{13\choose4}}{{52\choose4}}=4\times\frac{715}{270725} =0.01056\approx 0.01$

Thus, the probability that all four aces will be received by the same player is approximately 0.01.