We are given an experiment and want to represent the sample space by making a table. Then we want to find the probability P(6 and tails). The sample space of an experiment is the set of all possible outcomes. In this case, the sample space is the result of two stages.
Spinning a Spinner — 1, 2,3,4, or 5
Flipping a Coin — heads or tails
Keep in mind that there are several ways to make a table. The part that matters most is that the sample space ends up with all of the possible combinations. To make the table, we will list the outcomes of the first exercise in the first row and the outcomes of the second exercise in the left column.
Outcomes
1
2
3
4
5
Heads
Tails
Now we will pair each possible outcome from the first exercise with the possible outcomes from the second exercise.
Outcomes
1
2
3
4
5
Heads
1H
2H
3H
4H
5H
Tails
1T
2T
3T
4T
5T
Finally, we can find P(6 and tails). We can see that there are 10 total outcomes in the sample space and 0 of them are favorable.
Outcomes
1
2
3
4
5
Heads
1H
2H
3H
4H
5H
Tails
1T
2T
3T
4T
5T
We will use the Probability Formula to find the probability that P(6 and tails) occurs.
