Question

An organization will give a prize to a local artist. The artist will be randomly chosen from among 3 painters, 7 sculptors, and 12 photographers. What is the probability that the artist chosen will be a painter or a sculptor?
Write your answer as a fraction in simplest form.

Answer 1

To determine the probability that the artist chosen will be a painter or a sculptor, we first need to find the total number of artists and then the number of artists that fall into the painter or sculptor categories.

1. **Count the total number of artists:**
- Number of painters = 3
- Number of sculptors = 7
- Number of photographers = 12

The total number of artists is:
\[
3 + 7 + 12 = 22
\]

2. **Count the number of painters and sculptors:**
\[
\text{Number of painters} + \text{Number of sculptors} = 3 + 7 = 10
\]

3. **Calculate the probability:**
The probability \( P \) that the artist chosen will be a painter or a sculptor is the ratio of the number of favorable outcomes (painters or sculptors) to the total outcomes (all artists):
\[
P = \frac{\text{Number of painters or sculptors}}{\text{Total number of artists}} = \frac{10}{22}
\]

4. **Simplify the fraction:**
We can simplify \( \frac{10}{22} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[
\frac{10 \div 2}{22 \div 2} = \frac{5}{11}
\]

Thus, the probability that the artist chosen will be a painter or a sculptor is:
\[
\boxed{\frac{5}{11}}
\]