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?

Question

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: \[ \boxed{\frac{5}{11}} \]