Question

In the telemarketing industry, one successful sale in one hundred calls is considered success. That is, the probability of success is 1/100 and the probability of failure is 99/100 What is the probability of making 2 sales in 100 calls? Use your calculator.

Answer 1

0.1849 = 18.49% probability of making 2 sales in 100 calls

Explanation:

For each call, there are only two possible outcomes. Either it is a success, or it is not. The probability of a call being a success is independent of any other call. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

Probability of success is 1/100

This means that
`p = (1)/(100) = 0.01`

What is the probability of making 2 sales in 100 calls?

This is P(X = 2). So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 2) = C_(100,2).(0.01)^(2).(0.99)^(98) = 0.1849`

0.1849 = 18.49% probability of making 2 sales in 100 calls