Answered: From experience, the human resources…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

From experience, the human resources director of a certain company estimates that, for a particular job opening, 80% of the applicants are qualified. To help in the selection process, a test has been designed so that a qualified applicant has an 85% chance of passing the test, while an unqualified applicant has only a 5% chance of passing. An applicant is selected at random.

a. What is the probability that the applicant is qualified and will pass the test?

b. If the applicant passed the test, what is the probability that he or she is unqualified for the job?

Expert Solution

Step 1

Let us assume that Q=qualified

A=pass the selection process

Given that P(Q)=80%=0.80

P(A|Q)=85%=0.85

P(A|Q')=5%=0.05

Step 2

$The probability that the applicant is qualified and will pass the test is : P (Q and A) = P (Q) P (A | Q) = 0.80 \times 0.85 = 0.68 = 68 % Answer (a) : 0.68 or 68 %$

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