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*6^x/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