A car insurance company has determined that 9 of all drivers

A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 14-drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in car accident last year? A) 0.094 B) 0.906 C) 0.126 D) 0.393

Solution

Given X follows Binomial distribution with n=14 and p=0.09

P(X=x)=14Cx*(0.09^x)*((1-0.09)^(14-x)) for x=0,1,2,...,14

So the probability is

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

=1-14C0*(0.09^0)*((1-0.09)^(14-0))-...-14C2*(0.09^2)*((1-0.09)^(14-2))

=0.12551

Answer: C. 0.126