) What is the probability that there are no major cracks in two separate 5-mile stretches of  the highway?   (f) Given that there are no cracks in the first 5 miles inspected, what is the probability that  there are no major cracks in the next 10 miles inspected?   (g) If 10 separate one-mile stretches are considered, what is the probability that at least one  of the 10 stretches will contain at least one crack?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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The distance between major cracks in a highway follows an exponential distribution with a  mean of 5 miles.  

(e) What is the probability that there are no major cracks in two separate 5-mile stretches of  the highway?  

(f) Given that there are no cracks in the first 5 miles inspected, what is the probability that  there are no major cracks in the next 10 miles inspected?  

(g) If 10 separate one-mile stretches are considered, what is the probability that at least one  of the 10 stretches will contain at least one crack?  

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