A bank lobby has four video cameras positioned to view the e

A bank lobby has four video cameras positioned to view the entire lobby. Any one of the four is sufficient to monitor the lobby. Each camera functions independently and has a reliability of 0.91, that is, the probability of functioning is 0.91. A bank robbery takes place. Let a success (x) be defined as a camera functioning. Find the probability that the robbery was filmed, i.e., at least one camera functioning. (Round your answer(s) to 8 decimal places.)

Solution

Given X follows Binomial distribution with n=4 and p=0.91

P(X=x)=4Cx*(0.91^x)*((1-0.91)^(4-x)) for x=0,1,2,3,4

So the probability is

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

=1-4C0*(0.91^0)*((1-0.91)^(4-0))

=0.9999344