A drawing class was assigned a final project where students had to choose one art medium and one genre. The professor kept track of the types of projects submitted.Portrait LandscapeAcrylic paint 4 2Oil paint 4 12Charcoal 6 6What is the probability that a randomly selected student did not use oil paint or did not choose to create a landscape?Simplify any fractions.

To solve this problem, we first need to calculate the total number of students. We do this by adding up all the numbers in the table:

4 (acrylic portrait) + 2 (acrylic landscape) + 4 (oil portrait) + 12 (oil landscape) + 6 (charcoal portrait) + 6 (charcoal landscape) = 34 students

Next, we calculate the number of students who used oil paint and the number of students who chose to create a landscape:

Oil paint: 4 (oil portrait) + 12 (oil landscape) = 16 students Landscape: 2 (acrylic landscape) + 12 (oil landscape) + 6 (charcoal landscape) = 20 students

The probability that a randomly selected student used oil paint is 16/34 and the probability that a randomly selected student chose to create a landscape is 20/34.

The probability that a randomly selected student did not use oil paint is 1 - 16/34 = 18/34 = 9/17.

The probability that a randomly selected student did not choose to create a landscape is 1 - 20/34 = 14/34 = 7/17.

The question asks for the probability that a student did not use oil paint OR did not choose to create a landscape. In probability, "or" means we add the probabilities. However, we must be careful not to double count the students who neither used oil paint nor created a landscape.

So, we subtract the probability that a student did not use oil paint AND did not create a landscape. This is the probability that a student used acrylic paint or charcoal and created a portrait:

Acrylic or Charcoal: 4 (acrylic portrait) + 6 (charcoal portrait) = 10 students

The probability that a student did not use oil paint and did not create a landscape is 10/34 = 5/17.

So, the probability that a student did not use oil paint or did not choose to create a landscape is (9/17 + 7/17) - 5/17 = 11/17.