Question

Good performance (obtaining a grade of A+) in this probability class depends on your attendance (A) and completion of assignments (C). The probability that you will receive a grade of A+ are 95%, 75%, 50%, and 0%, if you attend the class and complete the assignments, if you attend but do not complete assignments, if you do not attend but complete assignments, and if you neither attend nor complete assignments, respectively. Further assume that if you attend the class, there is a 90% probability that you will complete the assignments. The probability that you will attend the class is 0.95 and the probability that you will complete the assignments is 0.90.

(a) What is the probability that you will receive an A+ in this class?

(b) If a student receives an A+, what is the probability that you attend the class and completed the assignments?

Answer 1

A = Attendance in class

C = completion of assignments

P(A) = 0.95 ; P(C) =.90 ; also P(C|A) = 0.90

P(A C)/P(A) = 0.90

P(A C) = 0.90*0.95 = 0.855

P(A C^') = P(A) - P(A C) = 0.95 - 0.855 = 0.095

P(A^' C) = P(C) - P(A C) = 0.90 - 0.855 = 0.045

P(A^' C^') = 1 - P(A U C) = 1- (P(A)+P(C)-P(A C)) =1 - (0.95+0.9-0.855) = 0.005

a) Probability of A+ grade = P(attend and complete and receive A+) + P(attend and not complete and receive A+) + P(not attend and complete and receive A+) + P(not attend and not complete and receive A+)

= 0.855*0.95 + 0.095*0.75 + 0.045*0.50 + 0.005*0 = 0.906

b) P(regularly attend and complete assignment given received A) =

P(attend and complete and receive A+ )/P(received A+) = (0.855*0.95)/0.906 = 0.8965