A test has 1 true false question and 2 multiple choice questions(A B C D). Draw a tree diagram and determine the sample space for the possible ways to answer the test.
To determine the sample space for the possible ways to answer the test, we can use a tree diagram.
First, let's start by drawing the first level of the tree diagram for the true/false question. Since there are only two possible answers, True or False, we will have two branches at this level:
T
|
F
Next, for each branch from the first level, we will draw the second level for the first multiple-choice question (A, B, C, D). Here, we will have four branches corresponding to the four choices:
T | F
| | |
A B C D
Finally, for each branch from the second level, we will draw the third level for the second multiple-choice question (A, B, C, D). Again, this will result in four branches for each choice:
T | F
| | |
A B C D A B C D
Now, we can determine the sample space by listing all the possible combinations of answers from the tree diagram:
1. T-A-A
2. T-A-B
3. T-A-C
4. T-A-D
5. T-B-A
6. T-B-B
7. T-B-C
8. T-B-D
9. T-C-A
10. T-C-B
11. T-C-C
12. T-C-D
13. T-D-A
14. T-D-B
15. T-D-C
16. T-D-D
17. F-A-A
18. F-A-B
19. F-A-C
20. F-A-D
21. F-B-A
22. F-B-B
23. F-B-C
24. F-B-D
25. A
26. B
27. C
28. D
29. F-D-A
30. F-D-B
31. F-D-C
32. F-D-D
So, the sample space for the possible ways to answer the test consists of 32 different combinations.