Question

determine the smaple space for an experiement 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.

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 ndn ndq ndd ddd ddq ddn dqd dqn dqq dnd dnq dnn

nnn nnq nnd 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 qdn qdd qnd qnd qnn

Answer 1

To determine the sample space for an experiment where a coin is selected from a bag containing a nickel (N), a quarter (Q), and a dime (D) three times with replacement, we can follow these steps:

1. **Identify the possible outcomes for one selection:** Each time we select a coin, we have 3 possible outcomes: N (nickel), Q (quarter), and D (dime).

2. **Determine the number of selections:** We are selecting a coin 3 times.

3. **Construct the sample space:** Since each coin selection is independent and we have 3 outcomes for each of the 3 selections, we can form the sample space by finding all possible combinations of outcomes.

There are \(3^3 = 27\) possible outcomes when selecting a coin 3 times:

- **First selection:** N, Q, D
- **Second selection:** N, Q, D
- **Third selection:** N, Q, D

The sample space can be represented as follows:
- nnn
- nnq
- nnd
- nqn
- nqq
- nqd
- ndn
- ndq
- ndd
- dnn
- dnd
- ddn
- dqq
- dqn
- dqd
- ddq
- qnn
- qnd
- qdn
- qqn
- qqd
- qdq
- qqq
- qdn
- qqd
- qnd
- qnn

Thus, the complete sample space is:

1. nnn
2. nnq
3. nnd
4. nqn
5. nqq
6. nqd
7. ndn
8. ndq
9. ndd
10. dnn
11. dnd
12. ddn
13. ddq
14. dqn
15. dqd
16. dqq
17. qnn
18. qnd
19. qdn
20. qqn
21. qqd
22. qdq
23. qqq
24. qdn
25. qqd
26. qnd
27. qnn

Thus, the sample space includes all the combinations of selecting coins from the bag three times.