To determine the correct sample space for the experiment of selecting a button (B, R, or Y) three times with replacement, we need to consider all possible outcomes for each selection.
Each selection can yield one of three buttons:
- B (blue)
- R (red)
- Y (yellow)
Since we perform this selection three times, the sample space consists of all combinations of these buttons across three selections. Each selection is independent because we are replacing the button back into the bag after each selection.
The total number of outcomes for three selections is given by \(3^3 = 27\), as there are three choices for each of the three selections.
Here are some of the combinations in the sample space:
- BBB
- BBR
- BBY
- BRB
- BRR
- BRY
- BYB
- BYR
- BYY
- RBB
- RBR
- RRR
- RRY
- RYB
- RYY
- YBB
- YBR
- YBY
- YRR
- YRY
- YYY
- YYB
- YYR
- RYB
- YRR
- RYR
- RYY
From the provided options, the sample space should contain 27 unique combinations consisting of all different permutations of B, R, and Y over three selections.
Thus, the valid option would correctly include combinations like BBB, RRR, YYY, etc., and contains no duplicates.
The correct sample space according to your selections might be:
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.
Since the options presented contained duplicates and did not correctly represent the unique outcomes produced in a three-selection scenario, you may want to choose the third response (with some combinations repeated), but each combination in a unique format from actual selections should still yield a total of \(3^3\) = 27.