math problem that i dont under stand

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

First you find the total number of artists, which is 3+7+12 =22. This number becomes the denominator. The probability that it is a painter is 3/22 and the probability it is a sculptor is 7/22. So you add the two probabilities because it is an or problem and you get 10/22. Then you reduce by dividing the numerator and denominator by the greatest common factor of 2 and you get 10/2=5, 22/2=11. The probability is 5/11 that the artist is a painter or a sculptor.