Suppose you are taking an assignment that adjusts its difficulty on later questi

Question

Suppose you are taking an assignment that adjusts its difficulty on later questions based on how well you do on previous questions. This assignment 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

Using the law of total probability, probability that we answer the second question correctly is computed as:

= Probability that we get the first answer correct * Probability that we get the second answer correct given that we got first answer correct + Probability that we get the first answer wrong * Probability that we get the second answer correct given that we got first answer wrong

= 0.65*0.4 + (1 - 0.65)*0.85

= 0.26 + 0.2975

= 0.5575

Therefore 0.5575 is the required probability here.

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