### Home > CCG > Chapter 9 > Lesson 9.1.1 > Problem9-12

9-12.

Gino looked around at the twelve students in his lunchtime computer science club and wrote down the following descriptions of their sex, clothing, and shoes:  Homework Help ✎

 male, long pants, tennis shoes male, shorts, tennis shoes female, shorts, tennis shoes male, shorts, other shoes female, dress or skirt, other shoes female, dress or skirt, tennis shoes female, long pants, tennis shoes male, long pants, other shoes male, long pants, other shoes female, shorts, other shoes female, long pants, other shoes male, long pants, tennis shoes
1. Make an area model or tree diagram of all the possible outfits in the sample space. Organize the combinations of sex, clothing, and shoes.

An area model can only have two events.

2. In your model or diagram from part (a), indicate the probabilities for each option. What is the probability that a randomly selected student is wearing long pants?

$\text{P(long)}=\frac{\# \text{ successes}}{\text{total }\#\text{ possible}}$

$\frac{1}{2}$

3. Which outcomes are in the event which is the union of {long pants} and {tennis shoes}? Which outcomes are in the intersection of {long pants} and {tennis shoes}?

This problem is easier to manage if you abbreviate each category.
For example, you can use M and F to abbreviate the gender categories.