Question

At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper. a. Find the probability that a course has a final exam or a research project. b. Find the probability that a course has NEITHER of these two requirements.

Answer 1

Answer:

a) $P(F UR) = P(F) +P(R) -P(F and R) = 0.72+0.46-0.32=0.86$

b) $P(FUR)' = 1-P(FUR)= 1-0.86 = 0.14$

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:

$P(F) = 0.72, P(R) =0.46$ 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:

$P(F UR) = P(F) +P(R) -P(F and R) = 0.72+0.46-0.32=0.86$

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:

$P(FUR)' = 1-P(FUR)= 1-0.86 = 0.14$

And that's the same value obtained with the diagram.