Chapter Closure
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How many branches does the tree diagram have? How many combinations does the area probability model have?
Color all the possible combinations of the area probability model that contains a piece of clothing that is black.
20 outfits
Diagrams: See solution.
2/5
Let's create the probability area model and tree diagram.
To draw a probability area model, we list the colors of one item of clothing on a vertical axis and the colors of the other item of clothing on a horizontal axis. The intersection of a vertical and horizontal color gives us an outfit.
To build a tree diagram, we will assume that Kiyomi first picks a pair of pants of a certain color. There are four different colored pants resulting in four branches. Next, she will pick a shirt of a certain color. There are five different colored shirts resulting in five more branches on each of the first four. All-in-all, we get the following tree diagram.
The number of outfits is the number branches at the end of the tree. From the diagram, we count a total of 20 branches.
To determine the probability of picking an outfit that includes a black item of clothing, we will mark all of these instances in the probability area model.
From the diagram, we see that there are 8 outfits that includes a black colored item of clothing. Therefore, the favorable outcomes are 8. From Part A, we know that the possible outcomes are 20. With this we can determine the probability for choosing an outfit with a black item of clothing. P(something black)&=8/20=2/5