1. ## negative binomial

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.

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I let x= 100, r= 1,

so

99C0 * (0.01)(0.99)^99, which gives 0.003967

2. 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.

3. 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.

4. Why are you multiplying by .01?

5. It's the formula for a negative binomial.

6. Formula for a negative binomial:

x-1 C r-1) (p^r)(1-p)^x-r

7. Originally Posted by amor_vincit_omnia
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,

so

99C0 * (0.01)(0.99)^99, which gives 0.003967

The probability that at least $100$ must be checked is the probability that the first $99$ are not defective, which is $0.99^{99} \approx 0.3697$

RonL

8. Originally Posted by amor_vincit_omnia
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.