youre at a clothing store that dyes your clothes while you wait. you get to pick from 4 pieces of clothing…

youre 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 youll end up with an orange hat?

youre 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 youll end up with an orange hat?

Answer

Explanation:

Step1: Calculate total combinations

The total number of combinations is the product of the number of clothing - items and the number of colors. There are 4 clothing - items and 3 colors, so the total number of combinations is $4\times3 = 12$.

Step2: Determine favorable combinations

There is only 1 favorable combination, which is an orange hat.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability of getting an orange hat is $\frac{1}{12}$.

Answer:

$\frac{1}{12}$