To find the probability of winning a prize in the art contest, we first need to determine the total number of prizes available and the total number of students participating.
- Total number of students: 50
- Number of prizes for first place: 1
- Number of prizes for second place: 1
- Number of prizes for honorable mention: 3
Total prizes available = 1 (first place) + 1 (second place) + 3 (honorable mentions) = 5 prizes.
Now, to find the probability of winning a prize, we can use the probability formula:
\[ \text{Probability of winning a prize} = \frac{\text{Number of prizes}}{\text{Total number of students}} \]
Plugging in the numbers:
\[ \text{Probability of winning a prize} = \frac{5}{50} = \frac{1}{10} = 0.1 \]
So, the probability of a student winning a prize in the art contest is \(0.1\) or \(10%\).