) 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?
) 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?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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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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