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In a multiple-choice test, an examinee either knows the correct answer with probability $\mathrm{p}$, or guesses with probability $1-\mathrm{p}$. The probability of answering a question
correctly is $\frac{1}{\mathrm{~m}}$, if he or she merely guesses. If the examinee
answers a question correctly, the probability that he or she really knows the answer is
Options:
correctly is $\frac{1}{\mathrm{~m}}$, if he or she merely guesses. If the examinee
answers a question correctly, the probability that he or she really knows the answer is
Solution:
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Verified Answer
The correct answer is:
$\frac{m p}{1+(m-1) p}$
Probability of knowing correct answer $=\mathrm{p}$ Probability to guess correct answer $=(1-\mathrm{p})\left(\frac{1}{\mathrm{~m}}\right)$
Probability to answer correctly $=\mathrm{p}+\frac{1-\mathrm{p}}{\mathrm{m}}$
So, required probability $=\frac{p}{p+\frac{1-p}{m}}=\frac{m p}{m p+1-p}$.
$=\frac{\mathrm{mp}}{1+\mathrm{p}(\mathrm{m}-1)}$
Probability to answer correctly $=\mathrm{p}+\frac{1-\mathrm{p}}{\mathrm{m}}$
So, required probability $=\frac{p}{p+\frac{1-p}{m}}=\frac{m p}{m p+1-p}$.
$=\frac{\mathrm{mp}}{1+\mathrm{p}(\mathrm{m}-1)}$
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