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)
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, 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

To determine the sample space for the given experiment, we need to consider all possible outcomes of selecting a coin from the bag three times, where each time the selected coin is replaced before the next selection.

There are three possible coins (Nickel-N, Quarter-Q, Dime-D) that can be chosen in each draw. Since the draws are independent and the coin is replaced after each selection, each draw is equivalent to making a choice among N, Q, and D.

To list all possible outcomes, we consider sequences of three selections.

Here is the step-by-step approach:

1. For the first selection, we have three possibilities: N, Q, D.
2. For the second selection, after replacing the coin, the same three possibilities exist: N, Q, D.
3. For the third selection, again, all three possibilities are available: N, Q, D.

So, the number of possible outcomes is [tex]\( 3 \times 3 \times 3 = 27 \)[/tex].

Now, let's systematically list all these possible outcomes:

1. First First coin: N
- Second coin: N
Third coin: N -> (NNN)
Third coin: Q -> (NNQ)
Third coin: D -> (NND)
- Second coin: Q
Third coin: N -> (NQN)
Third coin: Q -> (NQQ)
Third coin: D -> (NQD)
- Second coin: D
Third coin: N -> (NDN)
Third coin: Q -> (NDQ)
Third coin: D -> (NDD)

2. First coin: Q
- Second coin: N
Third coin: N -> (QNN)
Third coin: Q -> (QNQ)
Third coin: D -> (QND)
- Second coin: Q
Third coin: N -> (QQN)
Third coin: Q -> (QQQ)
Third coin: D -> (QQD)
- Second coin: D
Third coin: N -> (QDN)
Third coin: Q -> (QDQ)
Third coin: D -> (QDD)

3. First coin: D
- Second coin: N
Third coin: N -> (DNN)
Third coin: Q -> (DNQ)
Third coin: D -> (DND)
- Second coin: Q
Third coin: N -> (DQN)
Third coin: Q -> (DQQ)
Third coin: D -> (DQD)
- Second coin: D
Third coin: N -> (DDN)
Third coin: Q -> (DDQ)
* Third coin: D -> (DDD)

Listing these in a concise format:

[tex]\[ \text{{Sample Space}} = \{ \text{NNN}, \text{NNQ}, \text{NND}, \text{NQN}, \text{NQQ}, \text{NQD}, \text{NDN}, \text{NDQ}, \text{NDD}, \text{QNN}, \text{QNQ}, \text{QND}, \text{QQN}, \text{QQQ}, \text{QQD}, \text{QDN}, \text{QDQ}, \text{QDD}, \text{DNN}, \text{DNQ}, \text{DND}, \text{DQN}, \text{DQQ}, \text{DQD}, \text{DDN}, \text{DDQ}, \text{DDD} \} \][/tex]

Therefore, the total number of outcomes in the sample space is 27 and each sequence listed above comprises a unique element of the sample space.