00:01
For this problem to begin, we know that basically we're looking at a situation which would be labeled as a hyper -geometric random variable, where we have a population of size 14 with eight successes, and we're taking a sample of size 7.
00:31
And we want to find the probability of at most two successes.
00:41
Now, for a geometric random variable, we have that the probability, x is equal to some value k, it's given by, so let's see here, we can say this as, it's a little bit of a finicky formula to write out.
01:07
So we would have the number of successes, m, choose the number of successes in our sample, so choose k, times the number of non -success, so n minus m, choose the number of non -successes in our sample, so sample size minus the number of successes, divided by the total number of possible samples of size k, or pardon me, size n, rather, so big n choose little n.
01:38
So probability of x less than or equal to two, we can find using this formula, we just calculate out probability x equals 0, 1, and 2.
01:46
Now i'll note in my software here, if i write binomial, that is the same thing as saying choose, basically.
01:54
So if i want to have 14 choose, or actually i guess we should have 8 choose 0, which is really just one for what we're starting out with.
02:03
But we have 1 times now 14 minus 8, which would be 6, choose little n minus k.
02:13
So that would be.....