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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
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, 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

1 answer

To determine the sample space of the repeated experiment of selecting a button from the bag three times (with replacement), we can consider all possible outcomes.

Each time you select a button from the bag, you have three choices: Blue (B), Red (R), or Yellow (Y). When you're selecting a button three times, the selections are independent.

Thus, the outcomes for three selections are represented as ordered triples (where each position represents the result of one selection). The sample space consists of all combinations of the three colors for three selection events.

The total number of outcomes is \(3^3 = 27\), which can be listed as:

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

From the responses given, the second option contains the complete list of combinations for three selections. Therefore, the second response is the correct one:

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