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.
31. Rolling a pair of six-sided dice

31. Rolling a pair of six-sided dice

Accepted Answer

Welcome back, everyone. Our restaurant offers three types of sandwiches chicken CH, beef BF, and veggie VG and two types of bread white WH and wheat WT. If a customer randomly selects one sandwich and one type of bread, what is the sample space and how many possible meal arrangements are there? For this problem, we want to define a sample space, meaning all of the possible outcomes. So what we're going to do is simply analyze this problem. We have three types of sandwiches. It says CH BF, so let's list them and VG. And then we're selecting two types of bread, right? Either white or wheat, so that would be. WH and W T. And we want to identify all of the possible combinations to select. A sandwich and a bread, so we can begin with CH. We can go from CH and take WH. That will be our first possibility, so we can list it as CHWH. Then instead of going towards WH we can go towards WT and that will be our second possibility or second meal arrangements. We can write it as CH WT and we're done with CH. Which is chicken, right? And we're going to continue this process. So now for BF, that would be beef. We can choose WH which is white. So our next arrangement is BF WH followed by BF. W T. Let's list it BFWT. So we're done with beef, and finally, let's consider YG. Same idea here. We can choose WH or WT, so two additional possible arrangements. We can write it as VG WH. And the final possible arrangement is VGWT. So that would be our sample space. And now, the total number of arrangements would be 123456, right? Because those are all of the possible outcomes in our sample space. So, let's label our final answer and thank you for watching.

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