Four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not. The candidates are interviewed at random, and the first qualified candidate interviewed will be hired. The outcomes are the sequences of candidates that are interviewed. So one outcome is 2, and another is 431.

a. List all the possible outcomes.

b. Let A be the event that only one candidate is interviewed. List the outcomes in A.

c. Let B be the event that three candidates are interviewed. List the outcomes in B.

d. Let C be the event that candidate 3 is interviewed. List the outcomes in C.

e. Let D be the event that candidate 2 is not interviewed. List the outcomes in D.

f. Let E be the event that candidate 4 is interviewed. Are A and E mutually exclusive? Howabout B and E, C and E, D and E?

Answer :

Step 1 of 7 :

Given, four candidates interviewed for a job. Two of the four candidates are qualified,

The number 1 and 2 are qualified and other two numbered 3 and 4, are not qualified.

The candidates are interviewed randomly, and the first qualified candidate interviewed will be hired.

The outcomes are sequence of candidates that are interviewed. One outcome is 2 and another is 431.

Step 2 of 7 :

The claim is to list all possible outcomes.The outcomes are sequence of candidates that end with either 1 or 2

{ 1 , 2 , 31, 32, 41, 42, 341, 342, 431, 432.}

Therefore, we have 10 possible outcomes.

Step 3 of 7 :

b)

Let A be the event that only one candidate is interviewed.

The claim is to list the outcomes in A.

The outcomes in A are { 1 , 2 }

Step 4 of 7 :

c)

Let B be the event that three candidates are interviewed.

The claim is to list the outcomes in B.

The outcomes in B are { 341, 342, 431, 432.}