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 03-10-2017, 02:32 PM #1 DMMx69 old hand     Join Date: Jul 2006 Location: This Mortal Coil Posts: 1,678 Probability choosing combo of red/black balls from a pool, no replacement? I'm sure this is a simple solution, but it's not coming to me. I have a bag of 5 black balls and 3 red balls. I pull out 4 balls: 3 red and 1 black. I am NOT putting the pulled-out ball back in before the next choice. What is the chance of pulling various combos of red/black out, NOT replacing the ball each time? How can I generalize this problem? Thank you in advance.
 03-10-2017, 06:09 PM #2 heehaww Pooh-Bah     Join Date: Aug 2011 Location: It was an attractive goat in AR Posts: 4,182 Re: Probability choosing combo of red/black balls from a pool, no replacement? P(x red and y black) = C(3,x) * C(5,y) / C(8, x+y) It's just like if you were picking red/black cards from a deck.
 03-13-2017, 09:40 PM #3 Siegmund Pooh-Bah     Join Date: Feb 2005 Posts: 4,105 Re: Probability choosing combo of red/black balls from a pool, no replacement? In general the answer to "I pull n balls from a bag with B black balls and R red balls; how many are black?" is a Hypergeometric distribution.. In Wikipedia's notation, N=total number of balls, K=number of red balls, n=number of balls you draw, k=number of red balls you get. For your specific problem, as heehaww said, 4 black: 10 ways out of 56 3 black 1 red: 30 ways out of 56 2 black 2 red: 15 ways out of 56 1 black 3 red: 1 way out of 56 all 4 red obvious impossible.

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