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# Hypergeometric distribution question

I am just wondering if i can use hypergeometric distribution in a certain way. Lets say there are 10 balls in a basket: 5 blue, 3 green, 2 red. I am going to pick out 4, and i want to find the probability of picking out 2 reds, 1 green and 1 blue, in any order. So it could be RGRB, or BRRG, etc.

Could i find the probability by first finding the probability of getting 2 reds out of 4 picks using hypergeometric distribution, then 1 green out of 4, and then 1 blue out of 4. Then i would add the probabilities together?

It would be great if anyone could help me out, thanks!

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The hypergeometric distribution isn't even in the syllabus, but for the multivariate hypergeometric distribution, given a population of $N$, a sample size of $n$, a number of "types" of objects of $k$, the types denotes $y_i$, with $M_i$ objects for each type,
$P(y_1=x_1, y_2=x_2,... y_k=x_k)=\frac{{M_1 \choose x_1}{M_2 \choose x_2}...{M_k \choose x_k}}{{N \choose n}}$

where $\Sigma x_i =n,$ and $\Sigma M_i =N.$
$N=10, n=4, M_b=5, M_g=3, M_r=2, x_b=1, x_g=1, x_r=2$
$P(b=1, g=1, r=2)=\frac{{5 \choose 1}{3 \choose 1}{2 \choose 2}}{{10 \choose 4}}$
$=\frac{15}{210}$
$=7.143\%.$
You can't add the probabilities because they are not mutually exclusive events, so if you add them together given another case (for your case the result is less than 1) the probability would be greater than 1.
You can't directly multiply the probabilities because that way you would be counting each of the cases multiple times. For example for calculating P(r=2) you get $\frac{{2 \choose 2}{ 8 \choose 2}}{{10 \choose 4}}$, where $8 \choose 2$ should actually be $5\choose 1$ and $3 \choose 1$ which will be counted later when calculating P(b=1) and P(g=1).

Also: Checked the Pearson option 7 book (which features the hypergeometric distribution although it's not in the syllabus) to be sure, apparently their answer to 2.3-7a ii(a very similar question) is wrong as it applies for r1g1b2 instead of r1g2b1 as the question requests.

EDIT:

For LaTeX tags, you don't need to have a $sign. You're also using the wrong slash sign, \tex is what you're looking for. $Example$ So THAT's why... haven't been using /tex on html for a loooong time and I totally forgot how to use it. #### Share this post ##### Link to post ##### Share on other sites -snip- For LaTeX tags, you don't need to have a$ sign. You're also using the wrong slash sign, \tex is what you're looking for.

$Example$