Question

Theoretical Probabilities of Repeated Events Quick Check
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Question
Determine the sample space for an experiment where a coin is selected from a bag two times. The two coins placed in the bag are a nickel (N) and a quarter (Q). Each time a coin is selected, it is replaced before selecting the next coin.(1 point)
Responses

NN, NQ, QN
NN, NQ, QN

NN, NQ, QN, QQ
NN, NQ, QN, QQ

NN, QQ
NN, QQ

NQ, QN, NN, QN

Answer 1

In this experiment, a nickel (N) and a quarter (Q) are selected from a bag two times, and each time a coin is selected, it is replaced before the next selection.

The sample space consists of all the possible outcomes of selecting the coins. Since there are two selections and each selection can independently result in either a nickel or a quarter, we can list the outcomes as follows:

- Selecting a nickel first and then a nickel again: **NN**
- Selecting a nickel first and then a quarter: **NQ**
- Selecting a quarter first and then a nickel: **QN**
- Selecting a quarter first and then a quarter again: **QQ**

Putting it all together, the sample space is: **{NN, NQ, QN, QQ}**

Therefore, the correct response is:

**NN, NQ, QN, QQ**