A pipeline is to be inspected. There is a 10% chance that any 100ft section of...

A pipeline is to be inspected. There is a 10% chance that any 100ft section of pipeline will contain at least one defect (thinning walls, weld defect, etc). Assume the sections are independent (whether one sections fails or not is independent of whether other sections fail or not).
1. What is the probability that, given 2 defective sections have been found so far, that exactly 12 sections of pipeline have been inspected?
2. What is the probability that, given 50 sections have been inspected so far, that fewer than 5 defective sections have been found?
3. What is the probability that the first defect will be found in the 10^th pipeline inspected?
4. What is the average (expected) number of defects per 100 pipelines sections inspected?
5. Comment on the independence assumption. Do you believe this is a realistic assumption for a pipeline? Why or why not?

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orchestra answered 1 year ago

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