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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) Responses 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 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 RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, YYY, 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 RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, RRR, BBY, BBR, BYB, BYR, BYY, BRB, BRY, BRR, BBB, YYB, YYR, YBY, YBR, YBB, YRY, YRB, YRR RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, RRR, BBY, BBR, BYB, 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, BYR, BYY, BRB, BRY, BRR

1 answer

To determine the sample space for the experiment of selecting a button from a bag containing a blue (B), red (R), and yellow (Y) button, with the selection being repeated three times (with replacement), we can represent the outcomes of each selection as a string of three letters, where each letter corresponds to the color of the button selected.

Since there are three buttons and each selection does not affect the next (due to replacement), for each of the three selections, you have 3 choices: B, R, or Y.

Thus, the total number of possible outcomes, given that each of the three selections can independently be one of the three buttons, is calculated as:

\[ 3 \times 3 \times 3 = 27 \]

Now, we can list the possible combinations (strings of length 3) in the sample space:

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

The complete list covering all combinations is:

BBB, BBR, BBY, BRB, BRR, BRY, BYB, BYR, BYY, RBB, RBR, RBY, RRB, RRR, RRY, RYB, RYY, YBB, YBR, YBY, YRB, YRR, YRY, YYY, YYB, YYR.

Thus, the correct response 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.

This would be the complete and correct sample space for the repeated experiment.