Question

22% of all resumes received by a corporation for a management position are from females. 18 resumes will be received tomorrow.

What is the probability that exactly 1 resume will be from females?

Answer 1

5.80% probability that exactly 1 resume will be from females.

Explanation:

For each resume received by the corporation, there are only two possible outcomes. Either they are from a female, or they are not. The probability of a resume received being from a female is independent from other resumes. So 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.

22% of all resumes received by a corporation for a management position are from females.

This means that
`p = 0.22`

18 resumes will be received tomorrow.

This means that
`n = 18`

What is the probability that exactly 1 resume will be from females?

This is P(X = 1).

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

`P(X = 1) = C_(18,1).(0.22)^(1).(0.78)^(17) = 0.0580`

5.80% probability that exactly 1 resume will be from females.