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

Answer:

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

Step-by-step 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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.