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Probability that a student has passed in mathematics is $\frac{1}{4}$ and probability that he has passed in physics is $1 / 5$ . Probability that he has passed in both the subjects is $3 / 20$ . What is the probability that he has passed in mathematics if he has failed in physics ?

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$\frac{1}{8}$

$\frac{3}{16}$

$3 / 4$

$\frac{5}{8}$

answer is B.

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Detailed Solution

Prob that student is passed in mathematics $P (M) = 1 / 4$

Prob that students is passed in physics $P (P) = 1 / 5$

Prob. That student is passed in both the subject $P (M \cap P) = 3 / 20$

Required probability $= \frac{P (M \cap \vec{P})}{P (\bar{P})} \Rightarrow \frac{P (M) - P (M \cap P)}{1 - P (P)}$

$= \frac{\frac{1}{4} - \frac{3}{20}}{1 - \frac{1}{5}} = \frac{1 / 10}{4 / 5} = \frac{1}{8}$

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