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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, 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, NNN, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN, DDD, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN
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

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, 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

1 answer

To determine the sample space for the experiment of selecting a coin from a bag containing a nickel (N), a quarter (Q), and a dime (D) three times with replacement, you need to consider all possible sequences of selections.

Each selection can result in one of three outcomes (N, Q, or D), and since there are three selections made, the total number of combinations will be \(3^3 = 27\).

Here are all the possible outcomes:

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

Given the provided options, the choice that accurately lists all 27 outcomes is:

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

However, please note that this specific option was not provided verbatim in your options. Therefore, it's recommended to review all provided options closely to identify the one containing all unique combinations of N, Q, and D for three selections.