Question

A bag contains a blue button (B), a red button (R), and a yellow button (Y). If one button is selected and then returned to the bag three times, what is the sample space of the repeated experiment? (1 point)
RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, BBB, BBY, BBR, BYB,
BYR, BYY, BRB, BRY, BRR
RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, RRR, BBY, BBR, BYB,
O BYR, BYY, BRB, BRY, BRR, BBB, YYB, YYR, YBY, YBR, YBB, YRY, YRB,
YRR
RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, BBB, BBY, BBR, BYB,
O BYR, BYY, BRB, BRY, BRR, Yvy, YYB, YYR, YBY, YBR, YBB, YRY, YRB,
YRR
RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, YYY, YYB, YYR, YBY,
YBR, YBB, YRY, YRB, YRR

Answer 1

To determine the sample space for the experiment of selecting a button from a bag containing a blue button (B), a red button (R), and a yellow button (Y) three times (with replacement), we need to consider all possible combinations of selections over the three draws.

Since there are 3 possible buttons for each draw and we are drawing 3 times, the sample space will consist of every possible combination of these buttons across the three draws. Each position in a selection can either be B, R, or Y.

The combinations can be represented in terms of sequences of three selections, such as:

- BBB
- BBR
- BBY
- BRB
- BRR
- BYB
- BYR
- BYY
- RBB
- RBR
- RBY
- RRB
- RRY
- RYY
- YBB
- YBR
- YBY
- YRB
- YRR
- YYY
- YYY
- YRY
- ...
and more.

Since there are 3 options (B, R, Y) for each of the 3 selections, the total number of combinations can be calculated as:

3 (choices for the 1st button) × 3 (choices for the 2nd button) × 3 (choices for the 3rd button) = 3^3 = 27 combinations.

Thus, the correct sample space consists of 27 possible combinations (sequences) such as:

1. BBB
2. BBR
3. BBY
4. BRB
5. BRR
6. BYB
7. BYR
8. BYY
9. RBB
10. RBR
11. RBY
12. RRB
13. RRY
14. RYY
15. YBB
16. YBR
17. YBY
18. YRB
19. YRR
20. YYY
21. YRY
22. YRB
23. BRY
24. BYX
25. ...

So the sample space for this experiment is the set of all 27 possible outcomes with three button selections.

Looking at your provided options, none of them accurately represent the complete sample space as defined above. If you are supposed to identify a set that contains all these combinations, it looks like there is a typographical error since it is difficult to decipher the correct option under the provided texts.

The correct approach is to list from the theoretical outcome, which clearly states the defined sets of buttons in sequences of three.