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

To determine the probability of randomly picking an orange hat, we first need to assess the overall possibilities available when choosing a piece of clothing and a color.

1. **Choices of clothing:** There are 4 pieces of clothing: shirt, pants, socks, and hat.
2. **Choices of color:** There are 3 colors: purple, blue, and orange.

Now, we can calculate the total number of possible combinations of clothing and color:

\[
\text{Total combinations} = (\text{Number of clothing pieces}) \times (\text{Number of colors}) = 4 \times 3 = 12
\]

Next, to find the probability of picking an orange hat, we need to identify how many favorable outcomes exist for this specific event:

- There is only **1 favorable outcome** where you pick an orange hat (hat + orange).

Now, we can compute the probability:

\[
\text{Probability of picking an orange hat} = \frac{\text{Number of favorable outcomes}}{\text{Total combinations}} = \frac{1}{12}
\]

Thus, the probability that you'll end up with an orange hat is

\[
\boxed{\frac{1}{12}}.
\]