Identifying the Sample Space of a Probability Experiment In Ex...

Question

Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.
28. Identifying a person's eye color (brown, blue, green, hazel, gray, other) and hair color (black, brown, blonde, red, other).

28. Identifying a person's eye color (brown, blue, green, hazel, gray, other) and hair color (black, brown, blonde, red, other).

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a survey records a person's favorite fruit from the options of apple, grape, and orange, and their preferred beverage from water, juice, soda, and tea. What is the sample space for this experiment, and how many outcomes are in the sample space? So the first thing we're going to do is to determine our sample space for this experiment. So our sample space S is going to be equal to the set of basically all possible outcomes. So, we're going to do is pair each of our fruits with a beverage. So that means we're gonna have, for our first outcome, our first fruit is going to be apple, and we're gonna pair that with water. So we'll have apple and water. Then for our next outcome, we're gonna have apple with the second beverage, which is juice. For our third outcome, we'll have our apple. Paired with soda. And then finally we'll have the last outcome with an apple, we'll have an apple with T. Now we have to repeat this for the other two fruits. So then we'll have as another outcome, grape and water. Then we're gonna have Grape And juice. As the next outcome. Then we'll have Grape And soda And then we'll have Grape And tea. Then Um, make the combinations with our last fruit here. So we'll have, as an outcome, orange. Which is our next fruit. And water. Then we'll have an orange. With juice Then we'll have an orange. With soda And then finally, we'll have orange. And tea. So those are all the possible outcomes, and so that is going to be our sample space for this experiment. That is actually going to be the answer for the first half of this problem. Now for the second half, we need to determine how many outcomes are in the sample space. So now that we've written out the sample space. We can simply just count the number of outcomes that we have here, which when we count them, we have 12. We could also determine the number of outcomes by multiplying the number of fruits that we have by the number of beverages. So we'd have 3 multiplied by 4, which again is 12. So either way, we get the same answer. So the answer to the second half of this problem is going to be equal to 12. So, I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Sample Space

Outcomes

Tree Diagram

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