Question

Suppose we have a face recognition system with an accuracy of 90%. Suppose it is deployed in a security system that observes 40 people. Compute the following probabilities ( You should write down the expression mathematically, and an R expression that returns the answer ):

(a) It fails for exactly 6 people.

(b) It fails for at most 2 people.

(c) It fails for at least 8 people

Answer 1

Let , X be the number of people fails to face recognition system.

Let , 'p' be the probability that the people fails to face recognition system.

Here , X has a binomial distribution with parameter n=40 and p=0.10

Therefore , the probability mass function of X is ,

; x=0,1,2,.........,n and q=1-p

= 0 ; otherwise

(a) Now ,

By using R :
> dbinom(6,40,0.10)
[1] 0.1067562

(b) Now  

By using R :

> pbinom(2,40,0.10)
[1] 0.2228081

(c)

By using R :

1-pbinom(7,40,0.10)
[1] 0.04190194