Question

In a multiple-choice test, an examinee either knows the correct answer with probability P, or guesses with probability 1- P. The probability of answering a question correctly is 1m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

Answer 1

Correct option B. mp/(1 + p(m - 1))

Explanation:

P(he/she know correct answer) = p 

P(he/she guess correct answer) = (1 - p) × 1/m 

P(correct answer) = p + (1− p)/m 

P(he/she really know correct answer)

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

= mp/(1 + p(m - 1))