Question

The resumes of 2 male applicants for a college teaching position in computer engineering are placed in the same file as the resumes of 2 female applicants. 2 positions become available and the first, at the rank if the assistant professor is filled by selecting 1 of the 4 applicants at random. The second position, at the rank of instructor, is then filled by selecting at random 1 of the remaining 3 applicants.

1. How many elements are in a sample space S?

A) 4
B) 6
C) 8
D) 12
E) 16

2. How many elements of S are corresponding to event A that the position of assistant professor is filled by a male applicant?

A) 4
B) 6
C) 8
D) 12
E) 16

Answer 1

The resumes of 2 male applicants for a college teaching position in computer engineering are placed in the same file as the resumes of 2 female applicants. 2 positions become available and the first, at the rank if the assistant professor is filled by selecting 1 of the 4 applicants at random

Let two males be M1 & M2 .

Let two females be F1 & F2

(a) Elements are in a sample space S :

S={ M1M2 , M1F1 , M1F2 , M2M1 , M2F1 , M2F2 , F1M1 , F1M2 , F1F2 , F2M1 , F2M2 , F2F1 }

ANSWER is option(D)

(b)Elements of S are corresponding to event A that the position of assistant professor is filled by a male applicant :

It is easily shown in sample space S, i.e. 6 elements belongs to event A that the position of assistant professor is filled by a male applicant .

ANSWER is option(B)