Common Core Standards: Math
8b. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.
Students should be able to take compound probability situations and express them as organized lists, tables, and tree diagrams. For instance, students should be able to represent the sample space of spinning the two spinners below in list, table, or tree diagram form.
If necessary (and honestly, it'll probably be necessary), students should use the skills they gained in 7.SP.7 to develop a probability model in which each outcome has an equal likelihood. In this situation, we'll divide the yellow section in the first spinner into two equal events. We'll do the same with the red section in the second spinner. (Thanks, geometry!)
Now, students can create sample spaces in list, table, or tree diagram form by pairing an outcome from one spinner to an outcome of the other. Once all combinations are represented, students will have represented the entire sample space. If capital letters represent the outcome from the first spinner and lowercase ones represent the outcome from the second, they should create sample spaces that look something like this:
Organized List: Yy, Yr, Yr, Yb, Yy, Yr, Yr, Yb, Ry, Rr, Rr, Rb, By, Rr, Rr, Rb
All three methods of showing the sample space, clearly communicate that there are 16 outcomes in the sample space. The students can use any of these to start finding the probabilities of events such as spinning two reds, spinning exactly 1 blue, spinning a yellow on the first spinner and a blue on the second, and so on.