A deck of 52 playing cards is shuffled thoroughly and then divided into two piles, each with 26 cards. What is the probability that both piles contain exactly one ace (the Ace of Spades and the Ace of Hearts, for example)

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Topic: Probability Posted 1 year ago

A deck of 52 playing cards is shuffled thoroughly and then divided into two piles, each with 26 cards. What is the probability that both piles contain exactly one ace (the Ace of Spades and the Ace of Hearts, for example)? Hint: Consider the number of ways to choose one ace for each pile and divide it by the total number of ways the cards can be divided into two piles.

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Koala Tutor

Oct 2, 2023

Koala Ai Support

There are a total of $\binom{52}{26}$ ways to divide the cards into two piles. The number of successful outcomes is the number of ways to choose one ace for each pile, which is $\binom{4}{1} \binom{4}{1} = 4^2 = 16$. Therefore, the probability is $\dfrac{16}{\binom{52}{26}}=\boxed{\dfrac{16}{4950}}$.

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