I have a statistics problem, I have a feeling I'm going to feel incredibly stupid when someone tells me how to do it but I have spent a good hour trying to do this with no luck yet.

Ok there are 100 sweets in the bag. 15 are Dark Chocolate and 85 are Milk Chocolate.

Therefore probability of drawing one dark = 0.15

I need to work out:

If I pull 60 chocolates from the bag, with replacement, the probability of getting 16 Dark Chocolates out of 60 draws.

In the question set I have been given the answer 0.0077 and I have to work out how to get there.

I think I am right in thinking that if I wanted to know how to get 16 dark chocs in a row (replacing them each time) I would multiply 0.15*0.15*0.15... 16 times? But that still doesn't tell me the probability of getting 16 out of 60.
I tried 0.15 * 16/60 that is wrong.

I'm sure I am overlooking something simple but I can't work it out- please can anyone help or point me in the right direction.

Thanks Grace x

Try using a binomial probability.

In general, the probability of exactly k out of n with probability p is C(n,k)p^{k}(1-p)^{n-k}

In this case, n=60, k=16, p=.15, q=1-p=.85

C(60,16)(.15)^{16}(.85)^{44}=\frac{60!}{16!(44!)}( .15)^{16}(.85)^{44}