In a college, $30\%$ students fail in Physics, $25\%$ fail in Mathematics and $10\%$ fail in both. One student is chosen at random. The probability that she fails in Physics, if she has failed in Mathematics is

$\frac{2}{5}$

The correct answer is Option (2) → $\frac{2}{5}$ ##

Let $Ph$ and $M$ represent Physics and Mathematics students respectively.

$∴P(Ph) = \frac{30}{100} = \frac{3}{10}, P(M) = \frac{25}{100} = \frac{1}{4}$

$\text{and } P(M \cap Ph) = \frac{10}{100} = \frac{1}{10}$

$∴P(Ph|M) = \frac{P(Ph \cap M)}{P(M)} = \frac{1/10}{1/4} = \frac{2}{5}$