Probability of a 5 card hand containing exactly two spades

two0crew · #1 05-05-2005, 01:19 PM

This question was on a recent test for me and I am wondering what the answer is. I think I deduced it from the multiple choice answers but I was wondering logically how one would find out the probability that they would hold exactly two spades after being dealt 5 cards.

Thanks.

etgryphon · #2 05-05-2005, 01:49 PM

Isn't it:

x = [C(13,2) * C((50 - 11), 3)] / C(52, 5)

x = 0.2742797118847539

Mistakes?

-Gryph

LetYouDown · #3 05-05-2005, 01:50 PM

I came up with 27.4% in a very quick calculation.

LetYouDown · #4 05-05-2005, 01:52 PM

Looks the same as mine, except 13 C 2 instead of 13 * 12 (order doesn't matter). So, I came up with 1/2 of your number.

etgryphon · #5 05-05-2005, 01:55 PM

I edited it because I made a mistake. Now I got the same answer as you. I was double counting.

-Gryph