Question

Student A, B, and C get score F at the end of the probability course. However, kind
professor Lee decides to let one of them pass the course and the TA knows who is
the one but he can’t expose the secret. A still ask TA for the result, TA only tells
him/her that B will fail. A is so happy to know that because he/she thinks the
probability that he/she pass the class increase from 1/3 to 1/2. If A is right? If A is
wrong, what’s the probability for A and C to pass respectively?

I only have 20 chances per month to post question. I just have one already wasted when someone take magnetic's problem answer to answer my question. i'm just asking kindly to take time and read it if you can answer, answer it and thank you. if you cannot, please leave it so that someone else can. Thanks

Answer 1

P(TA told A that B will fail)=P(A will pass and TA told A that B will fail)+P(B will pass and TA told A that B will fail)+P(C will pass and TA told A that B will fail)=(1/3)*(1/2)+(!/3)*(0)+(1/3)*(1)=1/2

a)hence P(A will pass given TA told A that B will fail)=P(A will pass and TA told A that B will fail)/P(TA told A that B will fail)

=(1/3)*(1/2)/(1/2)=1/3

b) P(C will pass given TA told A that B will fail)=P(C will pass and TA told A that B will fail)/P(TA told A that B will fail)

=(1/3)*1/(1/2) =2/3