Question

A leak is detected on a certain section of pipeline that is 10 km long. To find the exact location of the leak, an inspection crew must travel along the pipeline and find the leak visually. Assume the leak is equally likely to occur anywhere along the 10 km stretch, and the inspectors will begin their tour starting at the east end of the stretch.

a) What is the probability that the inspectors will travel 3 km without locating the leak?

b)If the inspectors have traveled 3 km without finding the leak, what is the probability that they will find it within the next 2 km of their trip?

c) If the inspectors do not find the leak after the next 2 km, what is the probability that they will need to travel at least 4 km further before they find the leak?

Answer 1

The PDF of the distance from the east end of the stretch , where the leak is detected has PDF

The CDF is .

a)The required probability is

b) The required conditional probability is

c) The required conditional probability is