2, (16 points) Assume that a student has enjoyed 84% of all the classes he has t

Question

2, (16 points) Assume that a student has enjoyed 84% of all the classes he has taken at AUS. After he starts working part time as a student worker at the Dean's office, he works on a survey which lets him access to faculty evaluations. From this data, he finds out that, he did not enjoy 9 % of the courses that were taught by professors with good evaluations. Also, 70% of the courses he has taken were taught by professors with good evaluations a. What is the probability that the class was taught by a professor with good evaluations and that the student did not enjoy the class? What is the probability that the class was taught by a professor with poor evaluations and that the student enjoyed the class? What is the probability that the student had a professor with good evaluations if he did not enjoy the class? Suppose that a student signed up for three courses next semester, all of which are taught by professors with poor evaluations. What is the probability he enjoys all of them? b. c. d.

Explanation / Answer

here let good evaluation =P(G) and student enjoyed=P(E)

therefore from above P(E)=0.84 ; P(Ec|G) =0.09 ; P(G)= 0.70

a)P(good evaluation and did not enjoy) =P(G n Ec) =P(G)*P(Ec|G) =0.7*0.09=0.063

b) here P(G n E) =P(G)-P(G n Ec) =0.7-0.063 =0.637

hence P(poor evaluation and student enjoyed) P(Gc n E)=P(E)-P(G n E) =0.84-0.637=0.203

c)

P(G|Ec) =P(G n Ec)/P(Ec) =0.063/(1-0.84)=0.39375

d) P(enjoying course given that taught by professor of poor evaluation)=P(E|Gc) =P(E n Gc)/P(Gc) =0.203/0.3

=0.6767

hence P(he enjoy all 3 given taught by professor of poor evaluation) =(0.6767)3 =0.3098

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