Question
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
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
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
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
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
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
Answers
GPT-4o mini
To determine the sample space for the experiment of selecting a coin from a bag three times, with three types of coins (Nickel (N), Quarter (Q), and Dime (D)) and replacement after each selection, we can consider that each selection is independent and can result in one of the three coins.
Since you are selecting a coin three times, the sample space consists of all the possible combinations of these three selections. Each selection has 3 outcomes, and since there are 3 selections, the total number of outcomes in the sample space is \(3^3 = 27\).
The sample space can be represented as follows:
1. The first position can be N, Q, or D
2. The second position can be N, Q, or D
3. The third position can be N, Q, or D
By combining these possibilities, we obtain all the combinations:
- NNN, NNQ, NND, NQN, NQQ, NQD, NDN, NDQ, NDD
- DNN, DNQ, DND, DQN, DQQ, DQD, DDN, DDQ, DDD
- QNN, QNQ, QND, QQN, QQD, QDQ, QDN, QDD, QQQ
So, the complete sample space is:
NNN, NNQ, NND, NQN, NQQ, NQD, NDN, NDQ, NDD,
DDD, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN,
QQQ, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN
Now let’s inspect the provided options to find the one that accurately represents the sample space:
1. The first response is missing QQQ and contains repeats.
2. The second response is also missing combinations and does not have complete permutations.
3. The third response includes all combinations of N, Q, and D with the correct length but includes extraneous entries.
4. The fourth response contains duplicates.
The correct sample space should include each combination of N, Q, and D with each appearing three times. Therefore, the closest accurate response representing the complete sample space from the given answers does not seem to fully satisfy the condition. The right sample space, correctly formatted, would have all combinations as outlined above.
The most accurate choice out of the presented answers for best approximating the correct sample space would be the third response, but it still has some errors and duplication.
If you need a perfect sample space, list out or verify each unique entry to ensure accuracy.
Since you are selecting a coin three times, the sample space consists of all the possible combinations of these three selections. Each selection has 3 outcomes, and since there are 3 selections, the total number of outcomes in the sample space is \(3^3 = 27\).
The sample space can be represented as follows:
1. The first position can be N, Q, or D
2. The second position can be N, Q, or D
3. The third position can be N, Q, or D
By combining these possibilities, we obtain all the combinations:
- NNN, NNQ, NND, NQN, NQQ, NQD, NDN, NDQ, NDD
- DNN, DNQ, DND, DQN, DQQ, DQD, DDN, DDQ, DDD
- QNN, QNQ, QND, QQN, QQD, QDQ, QDN, QDD, QQQ
So, the complete sample space is:
NNN, NNQ, NND, NQN, NQQ, NQD, NDN, NDQ, NDD,
DDD, DDQ, DDN, DQD, DQN, DQQ, DND, DNQ, DNN,
QQQ, QQD, QQN, QDQ, QDN, QDD, QNQ, QND, QNN
Now let’s inspect the provided options to find the one that accurately represents the sample space:
1. The first response is missing QQQ and contains repeats.
2. The second response is also missing combinations and does not have complete permutations.
3. The third response includes all combinations of N, Q, and D with the correct length but includes extraneous entries.
4. The fourth response contains duplicates.
The correct sample space should include each combination of N, Q, and D with each appearing three times. Therefore, the closest accurate response representing the complete sample space from the given answers does not seem to fully satisfy the condition. The right sample space, correctly formatted, would have all combinations as outlined above.
The most accurate choice out of the presented answers for best approximating the correct sample space would be the third response, but it still has some errors and duplication.
If you need a perfect sample space, list out or verify each unique entry to ensure accuracy.