Problem 57P

Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with parameter λ = 3.

(a) Find the probability that 3 or more accidents occur today,

(b) Repeat part (a) under the assumption that at least 1 accident occurs today.

Solution 57P

Step1 of 3:

From the given problem we have a random variable ‘X’ it presents the number of accidents occurring on a highway each day. Here X follows poisson distribution with parameter

Here our goal is:

a). We need to find the probability that 3 or more accidents occur today.

b). We need to find the probability that at least 1 accident occurs today.

Step2 of 3:

a).

Here the random variable X follows poisson distribution with parameter Then, the probability mass function of poisson distribution is:

Consider,

Therefore, The probability that 3 or more accidents occur today is 0.5767.

Step3 of 3:

b).

The probability that at least 1 accident occurs today is:

Where,

[from part (a)]

Therefore, P(X1) = 0.9502.

Now,

Therefore, The probability that at least 1 accident occurs today is 0.6069.