I got one problem.
Out of deck of 52 cards we choose 20 cards and we return each card back into the deck. Count the probability that there will be 5 cards of clubs, diamonds, hearts, spades.
A - 5 cards of clubs
B- 5 cards of diamonds
C- 5 cards of hearts
D- 5 cards of spades
let N be the number of ways of getting 5 cards out of 13.
combinations with repetition:
N(A)=Binomial(13+5-1,5) = Binomial(17,5)=N(B)=N(C)=N(D)
Now I do this:
Assuming the experiments are independent (because we return the card in the deck):
I have probability P = Binomial(17,5) ^4 / Binomial(71,20)
These are combinations with repetition.
I get P = 0.0065059
But I tried the experiment with R Commander and it gives me P = 0.010666 with about 1 000 000 times throwing 20 cards.
So what is correct?
Thanks in advance.