A bag of marbles has equal numbers of gray (G), orange (O), and yellow (Y) marbles. A marble is picked from the bag and replaced, then a second marble is picked. Complete parts a and b. a. Represent the possible outcomes in the sample space. Determine the theoretical probability the marbles picked will not include yellow. b. If the experiment is repeated 350 times, how many repetitions can you expect to result in no yellow?

Let’s break this down step by step.

### Part a: Sample Space

Since there are three colors of marbles (Gray (G), Orange (O), and Yellow (Y)), when you pick one marble and then pick another (with replacement), the possible outcomes can be represented as pairs. Thus, the sample space ( S ) consists of the following outcomes:

1. (G, G)
2. (G, O)
3. (G, Y)
4. (O, G)
5. (O, O)
6. (O, Y)
7. (Y, G)
8. (Y, O)
9. (Y, Y)

So, the sample space is:

[ S = { (G, G), (G, O), (G, Y), (O, G), (O, O), (O, Y), (Y, G), (Y, O), (Y, Y) } ]

### Theoretical Probability of Not Including Yellow

To find the probability that the marbles picked will not include yellow, we first identify the outcomes that do not include yellow:

1. (G, G)
2. (G, O)
3. (O, G)
4. (O, O)

That gives us 4 outcomes without yellow. Since there are a total of 9 outcomes in the sample space, the probability ( P ) is calculated as follows:

[

P(text{