Calculating Probabilities for Multiple Colors of M&M's from a Bag

In summary, the conversation discusses the probability of pulling out specific colors of M&M's from a bag with known proportions. The suggested method to find the probability is through the use of a multivariate hypergeometric distribution, but there is also a possibility of using a multinomial distribution if the number of M&M's in the bag is assumed to be infinite.
  • #1
OneSquared
3
0
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!
 
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  • #2
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
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.
 

FAQ: Calculating Probabilities for Multiple Colors of M&M's from a Bag

What are binomial probabilities?

Binomial probabilities are used to calculate the likelihood of obtaining a certain number of successes in a series of independent experiments with two possible outcomes (usually labeled as success and failure).

How do you calculate binomial probabilities?

The formula for calculating binomial probabilities is: P(x) = (nCx)(p^x)(q^(n-x)), where n is the total number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1-p).

What is the difference between binomial probabilities and normal probabilities?

Binomial probabilities are used when there are only two possible outcomes (success or failure) in a series of independent experiments, while normal probabilities are used when there are more than two possible outcomes and the data follows a normal distribution.

What are some real-world applications of binomial probabilities?

Binomial probabilities are commonly used in fields such as statistics, genetics, and engineering to analyze and predict the likelihood of outcomes in various experiments and situations. They can also be applied in areas such as market research, quality control, and sports analytics.

What are some limitations of using binomial probabilities?

Binomial probabilities assume that each trial is independent and that the probability of success remains constant throughout all trials. In reality, these assumptions may not always hold, leading to inaccurate predictions. Additionally, binomial probabilities can only be used for discrete data, meaning that continuous data must be categorized into discrete categories before using this method.

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