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. Choose the correct answer below.
Click here to view sample space c.
Click here to view sample space b.
Click here to view sample space a.
Click here to view sample space d.
Determine the theoretical probability the marbles picked will not include yellow.
4/9
(Type an integer or a fraction.)
b. If the experiment is repeated 350 times, how many repetitions can you expect to result in no yellow?
repetitions (Round to the nearest whole number as needed.)
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{