Question

Assuming that a college is conducting a survey on student union activities. One of the questions on the survey asks students what they think of the quality of work the student union is doing on campus. The possible responses are excellent, good, fair and poor. Another question on the survey asks students how they feel about a proposed fee increase to help fund the cost of building a new student dorm. The possible responses to this question are favor, oppose and no opinion.

a) develop the sample space for someone who is responding to both questions.

b)show how a tree diagram can be used to display the outcomes listed in part a

Answer 1

a)

sample space for someone who is responding to both questions:

First question has 4 choices : Excellent, good, fair and poor

Second question has 3 choices : favor, oppose and no opinion

Total number of possible responses = 4 x 3 = 12

Sample space :

1 . Excellent, favor

2. Excellent, oppose

3. Excellent , no opinion

4 . Good, favor

5. Good, oppose

6. Good, no opinion

7. fair, favor

8. fair, oppose

9. fair, no opinion

10 . poor, favor

11. poor, oppose

12. poor, no opinion

b)show how a tree diagram can be used to display the outcomes listed in part a