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Determine the sample space for an experiment if a coin is selected from a bag three times. There are three coins in the bag: a nickel (N), a quarter (Q), and a dime (D). Each time a coin is selected, it is replaced before selecting the next coin.(1 point)

Responses

NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, DDD, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN, QQQ, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN
NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, DDD, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN, QQQ, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN

NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, QQQ, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN
NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, QQQ, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN

NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, DDD, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN
NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, DDD, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN

NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, NNN, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN, DDD, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN

1 answer

To determine the sample space for the experiment of selecting a coin from a bag that contains three coins (nickel N, quarter Q, and dime D) three times with replacement, we can think of the selections as sequences of three coins.

Each selection offers three choices: N, Q, or D. Therefore, for each of the three trials, there are 3 possibilities. Since there are 3 trials, the total number of combinations in the sample space can be calculated as: \[ 3 \times 3 \times 3 = 27 \]

We can list these combinations systematically as follows:

  1. NNN
  2. NNQ
  3. NND
  4. NQN
  5. NQQ
  6. NQD
  7. NDN
  8. NDQ
  9. NDD
  10. DNN
  11. DNQ
  12. DND
  13. DQQ
  14. DQN
  15. DQD
  16. DDD
  17. QNN
  18. QNQ
  19. QND
  20. QQQ
  21. QQD
  22. QQN
  23. QDQ
  24. QDN
  25. QDD
  26. QDD
  27. QND

Therefore, the correct response that lists all combinations is:

  • NNN, NNQ, NND, NQN, NQD, NQQ, NDN, NDQ, NDD, DNN, DNQ, DND, DQQ, DQN, DQD, DDD, QNN, QNQ, QND, QQQ, QQD, QQN, QDQ, QDN, QDD

From the responses you provided, the first option lists the combinations accurately.