Question

Hi there… I need some help help with this question.

Answer 1

ANSWERS

a. 1/2

b. 1001

c. 20

d. 8

e. 0.16

Step-by-step explanation

a. There are 4 women and 4 men on the hiring committee, which is a total of 8 people. The probability that a randomly selected person is a woman is,

`P(W)=(4)/(8)=(1)/(2)`

Hence, the probability that the person drawing the names from the hat is a woman is 1/2.

b. The applicant pool consists of 6 database administrators and 8 network engineers, which is a total of 14 applicants. We want to choose 4 applicants,

`_4C_(14)=(14!)/(4!(14-4)!)=(14\cdot13\cdot12\cdot11\cdot10!)/(4!\cdot10!)=(14\cdot13\cdot12\cdot11)/(4!)=1001`

Hence, there are 1001 ways to choose the group to be hired.

c. There is a total of 6 database administrators, and we want to choose 3,

`_3C_6=(6!)/(3!(6-3)!)=(6!)/(3!\cdot3!)=20`

Hence, there are 20 ways of choosing 3 database administrators.

d. There is a total of 8 network engineers, and we want to choose 1,

`_1C_8=(8!)/(1!\cdot(8-1)!)=(8\cdot7!)/(1\cdot7!)=8`

Hence, there are 8 ways of choosing 1 network engineer.

e. In part b, we found that there is a total of 1001 ways of choosing the 4 people to be hired. Also, in parts c and d, we found that there are 20 ways of choosing 3 database administrators and 8 ways of choosing 1 network engineer. The probability that this is the combination of people hired is,

`P(3DA+1NE)=(20\cdot8)/(1001)=(160)/(1001)\approx0.16`

Hence, the probability that the random selection of four persons to be hired will result in 3 database administrators and 1 network engineer is approximately 0.16.