Question

An experiment is performed where a 4-sided die is rolled and then a 4-color spinner is spun. The possible outcomes for each event are 1, 2, 3, and 4 for the 4-sided die and red (R), blue (B), yellow (Y), and green (G) for the 4-color spinner. Identify the sample space for this experiment.

Answer 1

Explanation:

Sample Space

The sample space associated with a random experiment is the set of all its possible outcomes. It's usually denoted by the letter
`\Omega`.

The experiment consists of rolling a 4-sided die and spinning a 4-color spinner. The possible outcomes for the die are

`D=\{1,2,3,4\}`

The possible outcomes for the spinner are

`S=\{R,B,Y,G\}`

Both events are independent, so any outcome from the die can be combined with any outcome from the spinner, thus the sample space is

`DxS=\left[\begin{array}{cccc}(1,R)&(1,B)&(1,Y)&(1,G)\\(2,R)&(2,B)&(2,Y)&(2,G)\\(3,R)&(3,B)&(3,Y)&(3,G)\\(4,R)&(4,B)&(4,Y)&(4,G)\\\end{array}\right]`