Question

An employer is looking to fill some positions, and several college graduates are interviewed. From past experience, we know that the employer will offer second interviews to 65% of the college graduates. Of those graduates offered second interviews, 70% of them will be hired. Only 5% of the college graduates not offered second interviews will be hired.

1. a) What is the probability of getting offered a second interview and not getting hired?

2. b) What is the probability of getting hired and not being offered a 2nd interview?

3. c) What is the probability of a randomly selected graduate (from the original group) being hired?

4. d) What is the probability of getting hired, given that a second interview was granted?

5. e) What is the probability of having had a second interview, given that someone was hired?

Answer 1

We are given here that:

P( second interview) = 0.65
Also, P( hired | second interview) = 0.7

Also, P(hired | no second interview ) = 0.05

a) Probability of getting offered a second interview and not getting hired is computed here as:

= P( second interview )P(not hired | second interview) = 0.65*(1 - 0.7) = 0.195

Therefore 0.195 is the required probability here.

b) The probability of getting hired and not being offered a 2nd interview is computed here as:

P( hired and no second interview) = P(no second interview)P(hired | no second interview)

P( hired and no second interview) = (1 - 0.65)*0.05 = 0.0175

Therefore 0.0175 is the required probability here.

c) Now the probability of a randomly selected graduate (from the original group) being hired is computed using law of total probability here as:

P( hired) = P( hired | second interview)P( second interview) + P(hired | no second interview )P(no second interview)

P(hired)= 0.7*0.65 + 0.05*0.35 = 0.4725

Therefore 0.4725 is the required probability here.

d) Now probability of getting hired, given that a second interview was granted is computed here as:

= P(hired | second interview) = 0.7

Therefore 0.7 is the required probability here.

e) The probability of having had a second interview, given that someone was hired is computed using Bayes theorem here as:

P( second interview | hired) = P( hired | second interview)P( second interview) / P(hired)

= 0.7*0.65 / 0.4725

= 0.9630

Therefore 0.9630 is the required probability here.