Probability help

[Goalie]

Here's the question:

You are buying plastic sheets from one of your suppliers.  Common problems with these sheets include warpage and chipped corners.
With probability 0.01, a sheet is both warped and also has chipped corners.
With probability 0.03, a sheet is warped, but with no chipped corners.
With probability 0.02, a sheet has chipped corners, but is not warped.
And, of course, with probability 0.94, a sheet is neither warped nor has a chipped corner.

You have just received a shipment of 1000 sheets.

a.)  Produce a formula for the probability that exactly 500 of the sheets are neither warped nor have chipped corners.

(There are more parts to this question, I just put this one down to start)

First off, please do not tell me the answer.

Second, would I use the Poisson distribution for this?  If so it should look something like this:

940⁵⁰⁰ e^-940 / 500!

Is this right?  or did I do something wrong?  Because the number I'm getting is 0, and that can't be.

Or do I use the Gaussian (normal) distribution?  What would that equation look like?

[BFM_Edison]

No, you use a binomial distribution, since it can either be neither warped nor have a chipped corner, or the opposite. Two possibilities, a set number of successes and a set number of failures, as well as the fact that you assumed that the sheets are independent of each other.

Anyways, considering you have 1000 sheets, it still is going to be a very low probability that it happens and will seem to be 0. At 1000, it's fairly similar to a continuous variable for the number of failures/successes, hence the drastically low probability.

[Goalie]

binomial, huh?

So it should look something like this:

(1000!/(500!*500!)) (.94)⁵⁰⁰ (.06)⁵⁰⁰

?

[BFM_Edison]

Yes, but look at the stuff I added talking about how it still will be very close to 0.

[BFM_Hydra]

Edison beat me to it while I was figuring out how to use my TI89 again

[BFM_Edison]

It will give you effectively 0, Hydra I should write a quick computer program to find the number and see if it can even handle it.

[Goalie]

Oh yeah, I understand that.  But when I use excel to process these large numbers that my calculator can't, it will at least give me something like 6.223x10^-23 instead of just 0.

Thanks.  If I have anymore problems I'll fling them by here again.

[BFM_Hydra]

(8.72132e^-628*1000!)/500!

AKA

undefined

[BFM_Edison]

Getting this to take a nonzero and finite value is hard work

[Goalie]

You don't have to solve the equation or anything.  The question is only asking for a formula, which is what I supplied earlier.

Though what you do beyond what I asked is up to you.  If you want to make that program, go ahead, but I don't need to know the answer because all I needed to do was show one step.

[BFM_Edison]

Ya, I know. But anyways, I'm getting the answer as somewhere around 5.14 x 10^-950 lol.

Actually, by hand, I approximate it at 10^-324.36.

[jim360]

I think you should be able to approximate the answer very well using the Normal Distribution with mean 60 and variance 56 (taken from the binomial distribution Bin(1000 , 0.06). Then your answer is given by putting those numbers into that formula and calculating the integral between 499 and 501. Hence your answer is ridiculously small since the expected number of faulty sheets, 60, is a full 60 standard deviations away from 500. This explains why everyone is getting an answer close to 0.