Q266 / 270 · NDA 2017 (Phase 2) · Mathematics
In a multiple-choice test, an examinee either knows the correct answer with probability 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
- A$\frac{\mathrm{mp}}{1+\mathrm{mp}}$
- Correct answerB$\frac{\mathrm{mp}}{1+(\mathrm{m}-1) \mathrm{p}}$
- C$\frac{(\mathrm{m}-1) \mathrm{p}}{1+(\mathrm{m}-1) \mathrm{p}}$
- D$\frac{(m-1) p}{1+m p}$
Solution
Probability of knowing correct answer $=p$
Probability to gues s 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 $=\frac{p}{p+\frac{1-p}{m}}=\frac{m p}{m p+1-p}$.
$=\frac{\mathrm{mp}}{1+\mathrm{p}(\mathrm{~m}-1)}$
Hence, the correct answer is option: 'B'.