Question

Suppose that the number of potholes per one city block in the Bywater area of New Orleans follow a Poisson distribution with an average of 2.5 potholes. Find the probability of at least 1 pothole in one city block of the Bywater.

Answer 1

Solution:

We are given

λ = 2.5

We have to find P(X≥1)

P(X≥1) = 1 - P(X=0)

P(X=x) = λ^x*exp(-λ)/x!

P(X=0) = 2.5^0 * exp(-2.5) / 0!

We have

2.5^0 = 1

0! = 1

Exp(-2.5) = 0.082085

P(X=0) = 2.5^0 * exp(-2.5) / 0!

P(X=0) = 1*0.082085 / 1

P(X=0) = 0.082085

P(X≥1) = 1 - P(X=0)

P(X≥1) = 1 - 0.082085

P(X≥1) = 0.917915

Required probability = 0.9179