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.
Prob(photographer) = 12/22 = 6/11
prob(painter or sculptor) = prob(not a phot.) = 1 - 6/11 = 5/11
Or
prob(painter) = 3/22
prob(phot.) = 7/22
prop(painter or phot.) = 10/22 = 5/11
To find the probability that the artist chosen will be a painter or a sculptor, we need to determine the total number of painters and sculptors, and divide it by the total number of artists.
First, we need to find the total number of painters and sculptors. There are 3 painters and 7 sculptors, so the total number of painters and sculptors is 3 + 7 = 10.
Now, let's find the total number of artists. There are 3 painters, 7 sculptors, and 12 photographers, so the total number of artists is 3 + 7 + 12 = 22.
Finally, we can calculate the probability by dividing the number of painters and sculptors by the total number of artists:
Probability = (Number of painters and sculptors) / (Total number of artists) = 10 / 22
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2 in this case:
Probability = (10 ÷ 2) / (22 ÷ 2) = 5/11
Therefore, the probability that the artist chosen will be a painter or a sculptor is 5/11.