Question

question 6 (essay worth 4 points) (sample spaces hc) part a: create your own experiment with 5 or more possible outcomes. (2 points) part b: create the sample space for your experiment in part a. explain how you determined the sample space. (2 points)

Explanation:

Step1: Define an experiment

Let the experiment be rolling two standard six - sided dice. The possible outcomes for each die are 1, 2, 3, 4, 5, 6.

Step2: Determine sample space

To find the sample space, we consider all possible pairs of outcomes. For the first die with 6 possible outcomes and the second die with 6 possible outcomes, by the multiplication principle, the size of the sample space \(S\) is \(n(S)=6\times6 = 36\). The sample space \(S=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}\). We determined the sample space by considering all possible combinations of the results of the two - die rolls.

Answer:

The experiment is rolling two standard six - sided dice. The sample space \(S=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}\) and it was determined by considering all possible combinations of the results of the two - die rolls.