Probability Of Colors and Clothes

Question

You're at a clothing store that dyes your clothes while you wait. you get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?

Answer 1

Let n be the total number of outfits.

n = (number of clothes)*(number of colors) = 4*3 = 12

Create a tree diagram. Pick one of the clothing (shirt, pants, socks, and hat) and one of the colors (purple, blue, and orange). You'll end up with these possible outcomes:

Purple shirt, blue shirt, orange shirt, purple pants, blue pants, orange pants, purple socks, blue socks, orange socks, purple hat, blue hat, and orange hat.

P(Orange Hat) = 1/12