Answer:
a)
b)
Step-by-step explanation:
Let's define the following events first:
F: The event that a course has a final exam.
R: The event that a course requires a research paper
From the info provided we have that:
P(F and R) =0.32
So then we can create a Venn diagram as we can see on the figure attached.
a. Find the probability that a course has a final exam or a research project.
For this case we can find the probability like this:
b. Find the probability that a course has NEITHER of these two requirements.
For this case we can use the complement rule and we can find the probability like this:
And that's the same value obtained with the diagram.
