An engineering company has four openings and the applicant pool consis

kdgg0909gn

kdgg0909gn

Answered question

2021-12-03

An engineering company has four openings and the applicant pool consists of 6 database administrators and eight network engineers. All are equally qualified so the hiring will be done randomly. The hiring committee consists of 4 women and 4 men.
a. If one person on the hiring committee is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a woman.
b. How many ways can the group who are to be hired be formed if they are no restrictions on composition?
c. How many ways can 3 database administrators be chosen?
d. How many ways can 1 network engineers be chosen?
e. What is the probability that the random selection of the four persons to be hired will result in 3 database administrators and 1 network engineer?

Answer & Explanation

John Twitchell

John Twitchell

Beginner2021-12-04Added 19 answers

Step 1- Writing given data
Given that
Number of job openings =4
Data base administrators =6
Network engineers =8
Hiring committee contains
Women =4
Men =4
We know that
Probability=Number of favorable eventsTotal number of events
Step 2 - Probability calculations
a. If one person on the hiring committee is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a woman.
Favorable events=Number of women=4
Total number of events=Both Men and Women=4+4=8
P(Women)=48=12=0.5
P(Women)=0.5
(b) How many ways can the group who are to be hired be formed if they are no restrictions on composition
Number of people to be hired =4
Total applicants =6+8=14
People of group size 4 is selected from total people of 14 in 14C4 ways.
14C4=14x13x12x114x3x2x1=1001ways
Number of ways to be hired is 1001 ways.
(c) How many ways can 3 database administrators be chosen ?
Total database administrators =6
3 database administrators be chosen from total 6 in 6C3 ways.
6C3=6x5x43x2x1=20ways
In 20 ways 3 database administrators be chosen .
(d) How many ways can 1 network engineers be chosen
Total network engineers =8
1 network engineers can be chosen from total 8 in 8C1 ways.
8C1=8ways.
In 8 ways 1 network engineer be chosen.
(e) What is the probability that the random selection of the four persons to be hired will result in 3 database administrators and 1 network engineer?
Favorable events = Selecting 3 database administrators and 1 network engineer from total 6 database administrators and 8 network engineers available.
Favorable events =6C3×8C1=20×8=160
Total number of events=Selecting four persons from total 14 applicants=14C4=1001
Probability=1601001=0.15984eq0.16
The required probability =0.16

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?