Problem 94 Solution

The number of potholes of miles of highway has a Poisson distristribution with a mean of 3. The number of potholes in two miles of highway would have a Poisson distristribution with a mean of 6. The probability of x potholes in two miles of highway is e-6*6x/x!.

The probability of 0 potholes is e-6*60/0! = e-6.

The probability of 1 pothole is e-6*61/1! = 6*e-6.

The probability of 2 potholes is e-6*62/2! = 18*e-6.

The probability of 3 potholes is e-6*63/3! = 36*e-6.

Take the sum the answer is 61*e-6 =~ 0.151204 .


This problem was taken from the May 1982 Actuary Exam 110, problem 20.

Michael Shackleford, ASA, August 17, 1999