Question

In: Statistics and Probability

There are a total of 17 people in an application pool, that are equally qualified for...

There are a total of 17 people in an application pool, that are equally qualified for a job. The pool consists of;

7 females and 10 males

There are 3 job openings for 3 different people. Type your answers as a decimal to 4 decimal places.

1. What is the probability that all 3 people are female?    

2. What is the probability that not all 3 people are female?    

3. What is the probability that none of the 3 people are female?    

4. What is the probability that two are female and 1 are male?

Solutions

Expert Solution

Number of people in application pool =17

Number of females =7

Number of males = 10

Number of job openings =3 (for 3 different people)

1.

Probability that all 3 people are female

= Number of ways of selecting 3 female from 7 female applicants / Number of ways of selecting 3 people from a pool of 17 people

Probability that all 3 people are female = 0.0515

2.

Probability that not all 3 people are female =1 - Probability that all 3 people are female

From 1. Probability that all 3 people are female = 0.0515

Probability that not all 3 people are female = 1-0.0515=0.9485

Probability that not all 3 people are female = 0.9485

3. Probability that none of the 3 people are female = Probability that all three people are male

= Number of ways of selecting 3 male from 10 male applicants / Number of ways of selecting 3 people from a pool of 17 people

Probability that all 3 people are male = 0.1765

Probability that none of the 3 people are female = 0.1765

4. Probability that two are female and 1 are male =

= Number of ways of selecting two female from 7 female applicants x Number of ways of selecting 1 male from 10 males / Number of ways of selecting 3 people from a pool of 17 people

Probability that two are female and 1 are male = 0.3088

orchestra answered 1 year ago
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