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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?

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). $\newline$ If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?

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Probability of simple events

Full solution

Q. 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).

\newline

If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?

Calculate Total Outcomes: First, let's figure out the total number of possible outcomes. Since there are $4$ pieces of clothing and $3$ colors, we multiply them together. $\newline$ $4$ pieces $\times$ $3$ colors $=$ $12$ total outcomes.
Find Favorable Outcomes: Now, we need to find the number of favorable outcomes, which is picking an orange hat. There's only one way to do this. $1$ orange hat.
Calculate Probability: To get the probability, we divide the number of favorable outcomes by the total number of possible outcomes. $\newline$ Probability = Number of favorable outcomes / Total number of possible outcomes $\newline$ Probability = $1$ orange hat / $12$ total outcomes $\newline$ Probability = $\frac{1}{12}$

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