In a multiple choice test an examinee either knows the correct answer with probability p or guesses ...........

Mathematics (NDA) Probability

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 1/m, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

$\frac{mp}{1+mp}$

$\frac{mp}{1+(m-1)p}$

$\frac{(m-1)p}{1+(m-1)p}$

$\frac{(m-1)p}{1+mp}$

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Explanation:

P(to know correct answer)=p
P(to guess correct answer)=(1-p)x(1/m)
P(to answer correctly)=p+ $\frac{1-p}{m}$
So, required probability = $\frac{p}{p+\frac{1-p}{m}}=\frac{mp}{1+p(m-1)}$