Question

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let be the probability that he knows the answer and be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability What is the probability that the student knows the answer given that he answered it correctly?

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Solution

Let,

The probability of student answer is

The probability of student guesses is

The probability of student answers correctly is

The probability that the student knows the answer, if he answered it correctly that is

The probability that student knows the answer is,

The probability that the student answer correctly, given that he knows the answer,

The probability that student guess the answer is,

The probability that the student answer correctly, given that he guesses,

Put these values in equation (1),

Thus, the required probability is

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