1 / 12 is the probability that you'll end up with an orange hat.
<u>Step-by-step explanation:</u>
Given that,
- There are 4 piece of clothing ⇒ shirt, pants, socks, or hat
- There are 3 possible colors ⇒ purple, blue, or orange
<u>To find the total number of outcome :</u>
Total outcomes ⇒ (number of clothes) × (number of colors)
⇒ 4 × 3 = 12
Therefore, there will be 12 different possibilities.
<u>The 12 different outcomes are :</u>
⇒ 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.
Now, the probability that you'll end up with an orange hat if you choose on random of 12 possibilities ⇒ No.of orange hats / Total no.of outcomes.
∴ P(orange hat) = 1 / 12
, where r is a residual. Plugging the pair into the formula, we obtain that 
and r=0.5