probability exercise with dependent events

I have some difficulties in solving the following problem:

A deck of 52 playing cards, containing all 4 aces, is randomly divided into 4 piles of 13 cards each. Define events E1, E2, E3, E4 as follows:

E1 = {the first pile has exactly 1 ace},

E2 = {the second pile has exactly 1 ace},

E3 = {the third pile has exactly 1 ace},

E4 = {the fourth pile has exactly 1 ace},

Use the formula

to find

the probability that each pile has an ace.

Re: probability exercise with dependent events

Looks like the product of four hypergeometrics

Quote:

Originally Posted by

**achacy** I have some difficulties in solving the following problem:

A deck of 52 playing cards, containing all 4 aces, is randomly divided into 4 piles of 13 cards each. Define events E1, E2, E3, E4 as follows:

E1 = {the first pile has exactly 1 ace},

E2 = {the second pile has exactly 1 ace},

E3 = {the third pile has exactly 1 ace},

E4 = {the fourth pile has exactly 1 ace},

Use the formula

to find

the probability that each pile has an ace.

That's how the first pile has exactly one ace and the rest has three.

So, now we have 3 aces and 39 total cards, so

That leaves us with 2 aces and 26 cards...

Finally we are stuck with a fourth pile that MUST have one ace...

The product of these probabilities should be the answer.

Re: probability exercise with dependent events

Thanks a lot for this help. It seems that I have to refresh my knowledge of combinatorics...

Re: probability exercise with dependent events

Thats just the basic hypergeometric, which is my next lecture in Probability on Tuesday.