Your final grade for a class depends on the results of two multiple choice exams

Question

Your final grade for a class depends on the results of two multiple choice exams. The first exam consists of 20 questions, each with 4 options, where each right answer is worth 5 points. The second exam consists of 25 questions, each with 5 options, and each right answer is worth 4 points. Note that each question only has one right answer. The final grade is calculated as the average of the two scores. a) Assuming you never study and just randomly pick options, what is your expected final score? Make sure you clearly define each random variable you use. b) Your friend was extremely sleepy during the first exam, and only had a 10% chance of picking the right option for each question. For the second exam, after studying fairly hard, they had an 80% chance of picking the right answer for each question. What is their expected final grade?

Explanation / Answer

a) expected final score = 20*0.25*5 + 25* 4*0.20 = 45 marks! ... b) 20*0.10*5 + 25* 4*0.80 = 90 Marks!!

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