With regard to the course of Statistics, of the Polytechnic Institute of Barcelo

Question

With regard to the course of Statistics, of the Polytechnic Institute of Barcelos Cock, it is known that 65% of students effectively study the curricular unit. Of these, it is known that 20% actively complain of this course. It is known that 65% of students, who do not study, also complain actively in the course. a) Find the probability of, selecting a student at random from the course, he actively complain of this course. b) Knowing that a student does not actively complain about the course, what is the probability that he did not study for this course?

Explanation / Answer

a)

P(complain) = P(studies actively)*P(complain/studies actively) +P(do not study)*P(complain/do not study)

= 0.65*0.2+0.35*0.65 = 0.3575

b)

P(does not actively complain) = P(studies actively)*P(does not actively complain/studies actively) +P(do not study)*P(does not actively complain/do not study) = 0.65*0.8+0.35*0.35 = 0.6425

P(did not study the course/does not actively complain)

= P(did not study the course and does not actively complain)/P(does not actively complain)

= 0.35*0.35/0.6425 = 0.19066

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