Question

The local auto parts shop has 14 batteries in stock. Four of them would work in a Toyota Camry. A person picks 2 batteries at random off the shelf. What is the probability that at least one of the batteries will work in a Toyota Camry?

Answer 1

We know that the total number of batteries are 14.

The probability that a battery would work in a Toyota Camry, or the probability of success = 4/14.

Thus, the probability of failure, q = 1-p = 10/14

We also know that the sample size, n =2.

This is a binomial distribution with n=2 and p=4/14.

We must find the probability that at least one of the two batteries will work in the Toyota Camry.

For this, we will find the probability that none of the batteries will work (that is, r=0) and then subtract this value from 1.

To find P(X=r), we must use

nCr * p^r *q^n-r

We know that r is 0, p is 4/14, q is 10/14 and n is 2.

Substituting these values in the equation, we get 0.51020406122.

Thus, the probability that at least one battery will work

= 1- 0.51020406122

= 0.4897959