Question

Two spinners are spun. One has 5 sections labeled Red, Orange, Purple, Yellow, and Green. The other has three sections labeled 1, 2, and 3. Find the Sample Space.

1. Create a tree diagram to show the outcomes for these two spinners.

Answer 1

Sample space:

`S = 15` possible outcomes

Tree diagram:

Observe the attached image.

Explanation:

For any experiment, the sample space of this experiment is the set of all the possible results of the experiment.

In this case we have two spinners. The first has 5 colors, by spinning the spinner you can get up to 5 different results. Therefore the sample space is
`S_1 = 5`

For the second spinner there are 3 possible results. By spinning the spinner you can get the numbers 1, 2 or 3. Then
`S_2 = 3`

Then, if the two spinners are rotated, the sample space would be:

`S = 5*3`

`S = 15` possible outcomes.

The tree diagram shown in the attached image shows the 15 possible results

{R, 1} {R, 2} {R, 3} {O, 1} {O, 2} {O, 3} {Y, 1} {Y, 2} {Y, 3} {P, 1} {P, 2} {P, 3} {G, 1}

{G, 2} {G, 3}