a. P(F ∪ R) = P(F) + P(R) - P(F ∩ R) = 0.72 + 0.46 - 0.32 = 0.86
b. P(F' ∩ R') = 1 - P(F ∪ R) = 1 - 0.86 = 0.14
. 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.
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