The probability that a machine produces a defective item is 0.01. Each item is check as it's produced. Assume these are independent trials and compute the probability that at least 100 items must be checked to find 1 defective item.
I let x= 100, r= 1,
99C0 * (0.01)(0.99)^99, which gives 0.003967
Wrong answer. Explain please.
I think what you found is the wrong probability.
What you are looking for is the probability that, after 99 items have gone by, you still haven't found a defective one. Then, anything that comes after it is irrelevant, because the first time you find a defective one, you will have checked at least 100 items.
So, you want to find the probability that you get 99 undefective items.
Well, if I dont multiply by the 0.01 I get the right answer.
But that's not what the question asks, or it doesn't seem so to me.
Why are you multiplying by .01?
It's the formula for a negative binomial.
Formula for a negative binomial:
x-1 C r-1) (p^r)(1-p)^x-r
You have calculated the probability of exactly 100 items checked before the first defective, rather than at least 100 items ........ There's a big difference.
Originally Posted by amor_vincit_omnia