Binomial probabilities

  • Thread starter OneSquared
  • Start date
  • #1
I have a bag of M&M's that is 22.5% Blue, 12.5%Brown, and 65% other.

If I pull 12 M&M's from the bag, what is the probabiliity that exactly 2 are blue and 3 are brown?

I used the binomial to find the probability of 2 blue and 3 brown, and I want to multiply them together to get the answer, but wouldn't that assume that the two are independent? Obviously they are not, because any time I pull out a blue M&M, it is one time I have not pulled out a brown M&M.

Can someone shed light on how to solve this? Thanks!
 

Answers and Replies

  • #2
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There is no replacement, so you can't use a multinomial distribution. You want a multivariate hypergeometric distribution. I found a formula on the web for it here:

http://www.agner.org/random/distrib.pdf
 
  • #3
375
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Correction - if you assume an infinite number of M&M's in the bag, then it's probably safe to use the multinomial distribution. The formula for that is also in the link I provided.
 

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