Question

Section L01 of GENG 200 has the following distribution of majors: 35% mechanical engineering, 25% electrical engineering, 25% civil engineering, and 15% computer science. The historical data shows that 10% of mechanical engineering majors, 7% of electrical engineering majors, 6% of civil engineering majors, and 15% of computer science majors get A grade in GENG 200.

i) (7.5 points) What is the probability that a randomly selected student is in an electrical engineering major and got an A grade in the course?

ii) (7.5 points) If a student name is selected randomly from the grade book of Section L01, what is the probability that the selected student got an A?

iii) (7.5 points) If a student is selected at random and his grade is A, what is the probability that he is in mechanical engineering major?

iv) (7.5 points) Calculate the probability that two students are selected at random and they are from two different majors.

Answer 1

a) probability that a randomly selected student is in an electrical engineering major and got an A grade in the course =0.25*0.07=0.0175

b)P( student got an A )=0.35*0.1+0.25*0.07+0.25*0.06+0.15*0.15=0.09

c)

probability that he is in mechanical engineering major given grade A

=P( mechanical engineering major and grade A)/P(grade A)=0.35*0.1/0.09=0.389

d)

probability that two students are selected at random and they are from two different majors

=1-P(they are both from same major)

=1-(0.35*0.35+0.25*0.25+0.25*0.25+0.15*0.15)=0.73