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

There are 7 painters, 4 sculptors, and 5 photographers. So total number of artists is \(7 + 4 + 5 = 16\).

Step2: Find number of painters or photographers

Number of painters is 7 and number of photographers is 5. So number of painters or photographers is \(7 + 5 = 12\).

Step3: Calculate probability

Probability is number of favorable outcomes (painters or photographers) divided by total number of outcomes (total artists). So probability is \(\frac{12}{16}\), which simplifies to \(\frac{3}{4}\) by dividing numerator and denominator by 4.

Answer:

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