A spinner has 3 equal sections colored blue, orange, and red. Determine the sample space for spinning the spinner two times.

Question

Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Blue Red
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Orange Blue
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Blue Blue
Red Blue
Red Orange
Red Red
Orange Blue
Orange Red
Orange Orange
Spin 1 Spin 2
Blue Orange
Blue Red
Red Blue
Red Orange
Orange Blue
Orange Red

Answer 1

To determine the sample space for spinning a spinner with 3 equal sections (blue, orange, and red) two times, we can represent the outcomes of the two spins as ordered pairs (Spin 1, Spin 2).

The possible outcomes for each spin are:

• Spin 1: Blue (B), Orange (O), Red (R)
• Spin 2: Blue (B), Orange (O), Red (R)

Since each spin has 3 possible outcomes, the sample space for spinning the spinner two times will contain all combinations of the outcomes from the first spin with the outcomes from the second spin.

We can list these combinations as follows:

1. (B, B)
2. (B, O)
3. (B, R)
4. (O, B)
5. (O, O)
6. (O, R)
7. (R, B)
8. (R, O)
9. (R, R)

Thus, the complete sample space for spinning the spinner two times is:

\[ S = { (B, B), (B, O), (B, R), (O, B), (O, O), (O, R), (R, B), (R, O), (R, R) } \]

This means there are a total of 9 outcomes in the sample space.