Tuesday, October 14, 2008

Math problem help

Looking for some general help on a math/probability problem. At one point I probably knew how to figure this out. Perhaps I should still know, but I can't seem to get it. I'm looking for a general way to figure out the following type of problem...

Given an infinitely (sufficiently) large population of marbles of which 10% are green and 90% are blue, what is the probability of picking 10 marbles of which exactly 3 are green?

I know the chance of picking one green marble is 0.1, and I know that the chance of picking 3 green marbles in a row is 0.001 (0.1 x 0.1 x 0.1). But I'm confused when it comes to figuring in that order is unimportant and that a finite number of marbles is being picked - clearly the chance of picking exactly 3 green marbles in 10 tries is different from picking exactly 3 green marbles in 100 tries. Any help? In the end I'd like to generalize the process - given a population of which X% are a given kind, what is the chance of subsampling exactly Y individuals in Z tries.

Thanks in advance...

4 comments:

Linda B. said...

Don't have the time to really sit and think about it right now... but intellectually I was thinking it would make it easier to figure it out with a 50-50 split in the distribution and then plug in the 30-70 split instead. Not sure if that makes sense or not. Wow, this gives us something to talk about on the way to Boston. We need to get a life.

gramps said...

(10!/3!x7!)(0.1)to the third power x (0.9)to the seventh power


if i remember by probability and combinatorials correctly

gramps said...

p.s.- did the math and it came out to 5.7%

Jim Lemire said...

Yup, I think that's it. I knew I needed to figure out the number of possible ways to achieve the particular combination of 3 and 7, but I was having trouble with the combinatorial part.

Thanks.