Question

In the card game bridge, each of 4 players is dealt a hand of 13 of the 52 cards. What is the probability that each player receives exactly one Ace?

Answer 1

@satellite73

Answer 2

I think its 4/52?

Answer 3

@kropot72 could u help please

Answer 4

I have seen an elegant method of solving it using slots. However my solution using the hypergeometric distribution gives the same result:
\[\large P(one\ ace\ each)=\frac{C(4, 1) \times C(48, 12)}{C(52, 13)}\times\frac{C(3, 1) \times C(36, 12)}{C(39, 13)}\]
\[\large \times \frac{C(2, 1) \times C(24, 12)}{C(26, 13)}\times 1=0.105\]

Answer 5

The slot method can be seen here:
https://www.math.ucdavis.edu/~gravner/MAT135B/materials/mat135a.pdf

Answer 6

but its wrong

Answer 7

Are you saying that the answer at the link is wrong? If so, why do you believe it is wrong?