# Probability - Expotential Distributions

The distance between major cracks in highway follows an exponential distribution with a mean of 5 miles.

a) What is the probability that there are no major cracks in a 10 mile stretch of highway.

b) What is the probability there is 2 major cracks in a 10 mile stretch of highway

c) what is the std deviation of the distance between major cracks

d) What is the probability that the first major crack occurs between 12 and 15 miles of the start of inspection.

e) What is the probability that there are no major cracks in two separate stretches of 5 miles of the highway.

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

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#### Solution Summary

Neat, step-by-step solution is provided for a problem with regards to probability and exponential distributions.