In a multiple choice exam with 20 questions, each question has 5 choices. For a

Question

In a multiple choice exam with 20 questions, each question has 5 choices. For a question chosen at random, the probability you know the answer is .7. When taking the exam, on a question for which you do not know the answer, you randomly select one of the 5 choices.

(a) What is the expected number of questions for which you know the answer?

(b) What is the expected number of questions you get correct?

(c) Given that you got a particular question correct, what is the probability you knew the answer to that question?

Explanation / Answer

a)

expected number of questions for which you know the answer = 20*0.7 = 14

b)

expected number of questions you get correct = 14+ 6*(1/5) = 14+ 1.2 = 15.2

c)

P(you knew the answer to a question given that you got it correct) = 14/15.2 = 0.9210

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