What is the Probability of Two Major Cracks in a 10 Mile Stretch of Highway?

[Andrew123]

Homework Statement

The distance between major cracks in the highway follows an exponential distribution with a mean of 5 miles. What is the probability that there are two major cracks in a 10 mile stretch of the highway?

Homework Equations

exponential dist: f(x) = Le(-Lx) where L = lambda (sorry i don't know latex)

E(X) = 1/L V(X) = 1/(L)^2

The Attempt at a Solution

well I'm abit stumped because the probability density function for the exponential dist tells us the time to an event etc.. not the number of events. So i really don't have much of an attempt :(

 

[Andrew123]

got it.. just use the poisson process.. with lambda = 2 etc.. answer is 0.2706