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: Calculate total number of artists

Total number of artists = number of painters + number of sculptors + number of photographers. So, \(7 + 4+ 5=16\) artists.

Step2: Calculate number of favorable outcomes (painters or photographers)

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

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So, \(P=\frac{12}{16}\)

Step4: Simplify the fraction

Divide numerator and denominator by 4. \(\frac{12\div4}{16\div4}=\frac{3}{4}\)

Answer:

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