Chapter Closure
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Diagrams: See solution.
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.
The number of outfits is the number of combinations in the sample space. By multiplying the number of colors in the horizontal direction by the number of colors in the vertical direction, we get the total number of outfits. 4 pants * 5 shirts = 20 outfits
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.
We assumed that Kiyomi first picked a pair of pants. However, we could also assume that she first picks a shirt and then pants. We would get the same number of outfits but the tree diagram would start with 5 branches and then an additional 4 branches on the first 5.
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