Question

Deb picks one marble from a bag. Then, she puts the marble back in the bag and picks a marble again. The bag has 1 yellow marble, 1 green marble, and 1 red marble.
Which table represents the sample space of this compound event?

Answer 1

To represent the sample space of Deb's compound event of drawing marbles from the bag, we first need to identify all possible outcomes. Since she picks a marble, replaces it, and then picks another marble, each pick is independent.

Given that the bag contains:
- 1 yellow marble (Y)
- 1 green marble (G)
- 1 red marble (R)

The possible outcomes for each pick are the same. In the first pick, Deb could select either Y, G, or R. After replacing the marble, she makes a second pick, which also has the same set of options. Therefore, we can represent the outcomes of two picks as ordered pairs.

The sample space can be represented as follows:

1. (Y, Y) - Yellow first, Yellow second
2. (Y, G) - Yellow first, Green second
3. (Y, R) - Yellow first, Red second
4. (G, Y) - Green first, Yellow second
5. (G, G) - Green first, Green second
6. (G, R) - Green first, Red second
7. (R, Y) - Red first, Yellow second
8. (R, G) - Red first, Green second
9. (R, R) - Red first, Red second

Thus, the sample space \( S \) for this compound event is:

\[
S = \{ (Y, Y), (Y, G), (Y, R), (G, Y), (G, G), (G, R), (R, Y), (R, G), (R, R) \}
\]

This table shows all possible outcomes resulting from Deb's two draws from the bag.