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

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

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

$\therefore$ $P\left( {\frac{{Ph}}{M}} \right) = \frac{{P(Ph \cap M)}}{{P(M)}} = \frac{{1/10}}{{1/4}} = \frac{2}{5}$