Probability question

Question

Under certain conditions, there is a 0.2 probability that a randomly selected driver will fail a driving test. If 2 randomly selected drivers are tested under these conditions, what is the probability that at least 1 will fail?

Answer 1

The probability that at least 1 will fail

= 1 - The probability that both pass

= 1 -(0.8)²

= 0.36

 

This is an application of the binomial distribution

P{X = k} = C(n,k)p^k(1-p)^n-k

 

The longer way to do this problem to illustrate the use of the above formula.

 

The probability that at least 1 will fail = The probability that one will fail + The probability that both will fail

P{X ≥ 1}= P{X = 1} + P{X = 2}

             = C(2,1)(0.2)¹(1-0.2)^2-1 + C(2,2)(0.2)²(1-0.2)^2-2

             = 2(0.2)(0.8) + (1) (0.2)² (1)

             = 0.36