We are given an experiment and want to represent the sample space by making a table. Then we want to find the probability P(even, tails, and odd). The sample space of an experiment is the set of all possible outcomes. In this case, the sample space is the result of three stages.
Spinning a Spinner — 1, 2, or 3
Flipping a Coin — heads or tails
Spinning a Spinner — 1, 2, or 3
Keep in mind that there are several ways to make a tree diagram. The part that matters most is that the sample space ends up with all of the possible combinations. Let's draw a tree diagram to represent the situation by combining the possible outcomes from each stage.
Finally, we can find P(even, tails, and odd). We can see that there are 18 total outcomes in the sample space. Also, spinning an even number means spinning a 2, and spinning an odd number means spinning a 1 or 3. Then there are only 2 favorable outcomes.
Favorable Outcomes
2, tails, 1
2,tails, 3
Let's substitute the two numbers into the Probability Formula and evaluate the quotient.
