Total Probability (2)

In a multiple choice question Exam, a student either knows the answer or he guesses. There are m options available in each question. If he guesses the answer, he is correct with 1/m probability.

Suppose p is the probability that he knows the answer and 1-p is the probability he doesn't know.

 

What is the probability that he has given answer correctly?

Answer

This is a case of Total Probability.

P(correct) = P(he knowns answer and answer is correct) + P(he guess the answer and answer is correct)

                      = p(1) + (1-p)*(1/m)

 

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