Question

At a college, 71% of courses have final exams and 43% of courses require research papers. Suppose that 26% of courses have a research paper and a final exam. Part (a) Find the probability that a course has a final exam or a research paper.

Answer 1

Answer:

There is an 88% probability that a course has a final exam or a research paper.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

E is the probability that a course has final exam.

P is the probability that a course requires research paper.

We have that:

$E = e + (E \cap P)$

In which e is the probability that a course has final exam but does not require research paper and $E \cap P$ is the probability that a course has both of these things.

By the same logic, we have that:

$P = p + (E \cap P)$

(a) Find the probability that a course has a final exam or a research paper.

This is

$Pr = e + p + (E \cap P)$

Suppose that 26% of courses have a research paper and a final exam.

This means that

$E \cap P = 0.26$

43% of courses require research papers.

So $P = 0.43$

$P = p + (E \cap P)$

$0.43 = p + 0.26$

$p = 0.17$

71% of courses have final exams

So $E = 0.71$

$E = e + (E \cap P)$

$0.71 = e + 0.26$

$e = 0.45$

The probability is

$Pr = e + p + (E \cap P) = 0.45 + 0.17 + 0.26 = 0.88$

There is an 88% probability that a course has a final exam or a research paper.