Respuesta :
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:
[tex]E = e + (E \cap P)[/tex]
In which e is the probability that a course has final exam but does not require research paper and [tex]E \cap P[/tex] is the probability that a course has both of these things.
By the same logic, we have that:
[tex]P = p + (E \cap P)[/tex]
(a) Find the probability that a course has a final exam or a research paper.
This is
[tex]Pr = e + p + (E \cap P)[/tex]
Suppose that 26% of courses have a research paper and a final exam.
This means that
[tex]E \cap P = 0.26[/tex]
43% of courses require research papers.
So [tex]P = 0.43[/tex]
[tex]P = p + (E \cap P)[/tex]
[tex]0.43 = p + 0.26[/tex]
[tex]p = 0.17[/tex]
71% of courses have final exams
So [tex]E = 0.71[/tex]
[tex]E = e + (E \cap P)[/tex]
[tex]0.71 = e + 0.26[/tex]
[tex]e = 0.45[/tex]
The probability is
[tex]Pr = e + p + (E \cap P) = 0.45 + 0.17 + 0.26 = 0.88[/tex]
There is an 88% probability that a course has a final exam or a research paper.
