Question

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? How about B and E, C and E, D and E?

Answer 1

a)
`\Omega=\{1, 2, 31, 32, 41, 42, 341, 342, 431, 432\}`

b) A={1, 2}

c) B={341, 342, 431, 432}

d) C={31, 32, 341, 342, 431, 432}

e) D={1, 31, 41, 341, 431}

f) E={41, 42, 341, 342, 431, 432}

Explanation:

We know that 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.

a) We get a set of all possible outcomes:

`\Omega=\{1, 2, 31, 32, 41, 42, 341, 342, 431, 432\}`

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

We get a set of all possible outcomes:

A={1, 2}

c) Let B be the event that three candidates are interviewed.

We get a set of all possible outcomes:

B={341, 342, 431, 432}

d) Let C be the event that candidate 3 is interviewed.

We get a set of all possible outcomes:

C={31, 32, 341, 342, 431, 432}

e) Let D be the event that candidate 2 is not interviewed.

We get a set of all possible outcomes:

D={1, 31, 41, 341, 431}

f) Let E be the event that candidate 4 is interviewed.

We get a set of all possible outcomes:

E={41, 42, 341, 342, 431, 432}

We conclude that the events A and E are mutually exclusive.

We conclude that the events B and E are not mutually exclusive.

We conclude that the events C and E are not mutually exclusive.

We conclude that the events D and E are not mutually exclusive.