# Binomial Probability problem.

## Homework Statement

10% of engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested, what is the probability that the first defective engine will be found between the 5th trial and the 25th trial, inclusive?

## The Attempt at a Solution

I believe this is just a binomial distribution with Bin(n,1) where n varies between 5 and 25.

$$\sum$$(nC1)(0.1)(.9)^(n-1)

This is way off because I am getting 6.47...

## The Attempt at a Solution

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tiny-tim
Homework Helper
Hi TheHamburgler1! No, it's just P(first is defective is the 5th) + … + P(first is defective is the 25th) Hi TheHamburgler1! No, it's just P(first is defective is the 5th) + … + P(first is defective is the 25th) Would we not express each of those via Bin(n,.1) where x=1? If not, how would we express one of them?

Thanks

Actually, this could be a Geometric distribution problem right? In that case we would sum x from 5 to 25 of (.1)(.9)^(x-1). This gives 0.5843102

tiny-tim
Yup! (and I assume you've used algebra to calculate that, and not 20 additions? )