A multiple-choice exam has 4 choices for each question. A student has studied en

Question

A multiple-choice exam has 4 choices for each question. A student has studied enough so that the probability they will know the answer to a question is 0.6, the probability that they will be able to eliminate one choice is 0.2. otherwise all 4 choices seem equally plausible. If they know the answer they will get the question right. If not they have to guess from the 3 or 4 choices. As the teacher I want the test to measure what the student knows. If the student answers a question correctly what's the probability they actually knew the answer?

Explanation / Answer

Probability that sutdent answered it correctly = 0.6 * 1 + 0.2 * 1/4 + 0.2*1/3 = 6/10 + 1/20 + 2/30 = ( 36+ 3+ 4) / 60 = 43/60;

Out of this 43/60, 6/10 or 36/60 comes from his knowing the correct answer; hence probability that he knew the answer given that he answered the question correctly = 36/60/43/60 = 36/43;

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