2. Suppose you are taking an exam that adjusts its difficulty on later questions

Question

2. Suppose you are taking an exam that adjusts its difficulty on later questions based on how well you do on previous questions. This exam has only two problems. The first problem is medium difficulty you think you have only a 65% chance of answering it correctly. If you get the first problem correct, then it asks a more difficult question that you have a 40% chance of answering correctly. On the other hand, if you answer the first question incorrectly, then it will ask an easier question that you have a 85% chance of answering correctly. What is the probability that you answer the second question correctly?

Explanation / Answer

Case 1:

First correct and second correct

P = 0.65 * 0.4 = 0.26

Case 2:

First incorrect and second correct

P = 0.35 * 0.85 = 0.2975

Total P = 0.5575

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