Question

The number of major faults on a randomly chosen 1 km stretch of highway has a Poisson distribution with mean 1.7. The random variable X is the distance (in km) between two successive major faults on the highway.
What is the probability you must travel more than 3 km before encountering the next four major faults?

Answer 1

The probability can be modeled using the following formula:
$P(X =3)$
wherein X follows the density 
$P(X=k)=\frac{1.7^ke^{-1.7}}{k!}$
Now for k = 3 we get:
$P(X=3)=\frac{1.7^3e^{-1.7}}{3!}=0.15$
The probability we are looking for is 0.15.
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