The number of workrelated injuries at a certain company in a

The number of work-related injuries at a certain company in a week has the Poisson distribution with mean 1/2. and the number of injuries for different weeks are independent. Find the probability that there are at least three work-related injuries in a four week period.

Solution

Given X follows Poisson distribution with mean=0.5*4 = 2

P(X=x)=(2^x)*exp(-2)/x! for x=0,1,2,...

So the probability is

P(X>=3) =1-P(X=0)-P(X=1)-P(X=2)

=1-(2^0)*exp(-2)/1-(2^1)*exp(-2)/1-(2^2)*exp(-2)/2!

=0.3233236