Ask a New Question
Menu

Bivariate Data Analysis & Probability Unit Test

12 of 1612 of 16 Items

Question
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, 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
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, 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

1 answer

In this problem, we need to find the sample space for selecting coins from a bag three times, with replacement. The bag contains three different coins: a nickel (N), a quarter (Q), and a dime (D).

Since each coin is replaced after selection, each of the three selections is independent and can be any of the three coins. Therefore, the total number of outcomes for this experiment can be calculated as follows:

For each selection, there are 3 choices (N, Q, or D). Since there are 3 selections made, the number of possible outcomes can be expressed as \(3^3 = 27\).

The complete sample space of all possible outcomes would consist of all combinations (repetition allowed) of the three coins over the three selections. The sample space can be represented as follows:

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

It appears that your response lists many of these combinations but may also include duplicates or be structured differently than expected, making certain responses incorrect.

The complete sample space in the correct format is represented by the response that captures all 27 unique combinations of the selections without duplicates or omissions.

From the provided options, the second option appears to provide the full set with some duplicates guessed. However, only the correct complete combinations must be considered without duplication in the listing.

The correct answer should incorporate all combinations without repetition, and given the refined definitions, the best output would be the one with all different combinations without missing any valid combinations from the expected list of 27. Thus, I'd recommend reviewing the options to ensure they contain the full unique set without omission.

Let me know if you need further clarity on this topic!