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 March 18th, 2011, 03:55 PM #1 Member   Joined: Aug 2009 Posts: 69 Thanks: 0 Probability practice problems? Soz... I have an important standardized test tomorrow... and usually these things are really easy, but I've forgotten most of the stuff I've learned about probability. One question that really tripped me up: You have 6 white marbles, 4 green marbles, and 5 blue marbles in a bag. If you draw four marbles at random, what's the probability of getting at least one of each color? So... how do you solve this question? And what are some good websites for practicing probabilities?
 March 21st, 2011, 06:47 AM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Probability practice problems? You need the generalized hypergeometric formula. If you pick n out of N things, and of those a out of A of the first sort, b out of B of the first sort, etc (so a+b+c+... = n, and A+B+C+... = N) then the probability is $\frac{\binom{A}{a}\binom{B}{b}\binom{C}{c}...\bino m{Z}{z}}{\binom{N}{n}}$ In this case you pick 1 white, 1 green, 2 blue, OR 1 white, 2 green, 1 blue, OR 2 white, 1 green, 1 blue. $\frac{\binom{6}{1}\binom{4}{1}\binom{5}{2}+\binom{ 6}{1}\binom{4}{2}\binom{5}{1}+\binom{6}{2}\binom{4 }{1}\binom{5}{1}}{\binom{15}{4}}= \frac{6.4.10+6.6.5+15.4.5}{1365}=\frac{720}{1365}= \frac{48}{91}$

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