Question

At a college, 69% of the courses have final exams and 42% of courses require research papers. Suppose that 29% of courses have a research paper and a final exam. Let F be the even 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 paper. Your answer is : (b) Find the probability that a course has NEITHER of these two requirements. Your answer is :

Answer 1

The probability that a course has a final exam or a research paper is 0.86. The probability that a course has neither of these two requirements is 0.14.

Step-by-step explanation:

To find the probability that a course has a final exam or a research paper, we can use the principle of inclusion-exclusion. The probability that a course has a final exam is 0.72, the probability that a course requires a research paper is 0.46, and the probability that a course has both a final exam and a research paper is 0.32.

The probability that a course has a final exam or a research paper is given by:

P(F or R) = P(F) + P(R) - P(F and R)

= 0.72 + 0.46 - 0.32 = 0.86

Therefore, the probability that a course has a final exam or a research paper is 0.86.

To find the probability that a course has neither of these two requirements, we can use the complement rule.

The probability that a course has neither a final exam nor a research paper is given by:

P(neither F nor R) = 1 - P(F or R)

= 1 - 0.86 = 0.14

Therefore, the probability that a course has neither a final exam nor a research paper is 0.14.