OT: Probability Question (no poker).
 

To all the qualified mathematician types out there:

Note: This is NOT a homework assignment. A friend asked me this (having to do with quality assurance), and I don't quite know how to respond.

Say I have a grid of N light bulbs. I test S of them to see if they work. I find that F of the tested bulbs fail. How do I come up with the probability P_K that a total of K (from the total N) bulbs fail? If I then compute P_K for 0 <= K <= N, I will then have a discrete probability distribution describing K failures given that I tested S bulbs and found F failures. I think this is what I want so that I can get a good idea of how accurate my "sampled testing" is. Is this the right/wrong approach?

Anyone want to give this a shot?

I have considered estimating the distribution psuedo-empirically by running computer simulations, but if there is a faster closed formula, I am all ears.

Thanks in advance,
RMJ