Question

an organization will give a prize to a local artist. the artist will be randomly chosen from among 7 painters, 4 sculptors, and 5 photographers. what is the probability that the artist chosen will be a painter or a photographer?
write your answer as a fraction in simplest form.

Explanation:

Step1: Find total number of artists

To find the total number of artists, we add the number of painters, sculptors, and photographers. So, total artists = \(7 + 4 + 5\)
\(7+4 + 5=16\)

Step2: Find number of painters or photographers

The number of painters or photographers is the sum of the number of painters and the number of photographers. So, number of painters or photographers = \(7+5\)
\(7 + 5=12\)

Step3: Calculate the probability

Probability is the number of favorable outcomes (painters or photographers) divided by the total number of possible outcomes (total artists). So, probability \(=\frac{\text{Number of painters or photographers}}{\text{Total number of artists}}\)
\(\frac{12}{16}\)

Step4: Simplify the fraction

We simplify \(\frac{12}{16}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. \(\frac{12\div4}{16\div4}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)