his probability class depends ony dance (A) and completion of assignments (C). T

Question

his probability class depends ony dance (A) and completion of assignments (C). The probabilities that you will receive a grade of A+ are 100%, 70%, 50%, and 0%, if you regularly attend and complete the assignments. if you regularly attend but do not complete the assignments, if you do not regularly attend but complete the assignments regularly, and if you neither attend nor complete assignments, respectively. Further assume that if you attend the class regularly, there is a 90% probabil- ity that you will complete the assignments. The probability that you will attend the class reg- ularly 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 you received an At, what is the probability that you regularly attended the class and completed the assignments?

Explanation / Answer

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

hence P(AnC)/P(A) =0.90

P(AnC) =0.9*0.95=0.855

P(AnCc) =P(A)-P(AnC) =0.95-0.855 =0.095

P(AcnC) =P(C)-P(AnC) =0.90-0.855 =0.045

P(AcnCc) =1-P(AUC) =1-(P(A)+P(C)-P(AnC)) =1-(0.95+0.9-0.855)=0.005

hence probability of A+ grade =P(attend and complete and receive A+ +attend and not complete and receive A+ +not attend and complete and receive A+ + not attend and not complete and receive A+ )

=0.855*1+0.095*0.7+0.045*0.5+0.005*0=0.944

b)

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

P(attend and complete and receive A+ )/P(received A+) =0.855*1/0.944=0.90572

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