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:  

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.

   Hint (a):

   An area model can only have two events.

   More Help (a):

   

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?

   Hint (b):

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

   Answer (b):

   $\frac{1}{2}$

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}?

   Hint (c):

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