Question

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


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 need to consider all possible combinations of outcomes for each spin.

Since each spin can result in one of three colors (Blue, Orange, or Red), the total number of possible outcomes for two spins can be calculated as follows:

- For the first spin, there are 3 possible outcomes (Blue, Orange, Red).
- For the second spin, there are also 3 possible outcomes (Blue, Orange, Red).

The sample space for spinning the spinner two times can be represented as pairs of outcomes where the first element is the result of the first spin and the second element is the result of the second spin. Therefore, we can enumerate the sample space:

1. (Blue, Blue)
2. (Blue, Orange)
3. (Blue, Red)
4. (Orange, Blue)
5. (Orange, Orange)
6. (Orange, Red)
7. (Red, Blue)
8. (Red, Orange)
9. (Red, Red)

Thus, the sample space \( S \) is:

\[
S = \{ (Blue, Blue), (Blue, Orange), (Blue, Red), (Orange, Blue), (Orange, Orange), (Orange, Red), (Red, Blue), (Red, Orange), (Red, Red) \}
\]

This gives us a total of \( 3 \times 3 = 9 \) possible outcomes when spinning the spinner two times.