To determine the sample space of the repeated experiment where a button is selected and returned to the bag three times, we can assess all possible outcomes.
Given that there are three buttons (B, R, Y), each selection can result in any of the three buttons, and each selection is independent due to replacement. When selecting a button three times, the total number of outcomes will be \(3^3\) because there are 3 options for each of the 3 selections.
The sample space consists of all possible combinations of the buttons over the three selections. This means we list all combinations where each position in the outcome can be B (blue), R (red), or Y (yellow).
The correct sample space will include the following combinations:
- RRR
- RRY
- RRB
- RYR
- RYB
- RYY
- RBR
- RBY
- RBB
- YRR
- YRY
- YRB
- YYY
- YYB
- YYR
- YBY
- YBR
- YBB
- BRR
- BRY
- BRB
- BBB
- BBY
- BBR
- BYB
- BYR
- BYY
When you list out again carefully, you will find the complete set should include all these combinations clearly.
Now, review the provided options. The option that matches this comprehensive list is:
RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, BBB, BBY, BBR, BYB, BYR, BYY, BRB, BRY, BRR, YYY, YYB, YYR, YBY, YBR, YBB, YRY, YRB, YRR
Make sure to count that indeed all combinations of (B, R, Y) over 3 trials are correctly listed in your selected option.