Two students, X and Y, forgot to sign their exam papers. Professor knows that th

Question

Two students, X and Y, forgot to sign their exam papers. Professor knows that they can write a good exam with probabilities 0.8 and 0.4, respectively. After grading, he notices that one unsigned exam is good and the other is bad. Given this information, and assuming that students worked independently of each other, what is the probability that the good exam belongs to student X?

Hi, I already know that the answer is 6/7, but I'm not sure how to actually arrive at this answer, and this is what I need help with, so please leave a detailed solution

Explanation / Answer

Yes, you are correct. 6/7 is the correct answer. Probability X Good and Y Bad = (.8)(1-.4) = 12/25 Probability Y Good and X Bad = (1-.8)(.4) = 2/25 (Probability X Good and Y Bad) / [ (Probability X Good and Y Bad ) + (Probability Y Good and X Bad )] (12/25)/[(12/25)+(2/25)] = 12/(12+2) = 12/14 = 6/7 Rating appreciated!

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