Question

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 failed in Mathematics is

(a) $\frac{1}{10}$
(b) $\frac{2}{5}$
(c) $\frac{9}{20}$
(d) $\frac{1}{3}$

Answer 1

(b) Here, $P_{\left(Ph\right)}=\frac{30}{100}=\frac{3}{10},P_{\left(M\right)}=\frac{25}{100}=\frac{1}{4}$
and $P_{(M\cap Ph)}=\frac{10}{100}=\frac{1}{10}$
$\therefore P\left(\frac{Ph}{M}\right)=\frac{P(Ph\cap M)}{P\left(M\right)}=\frac{\frac{1}{10}}{\frac{1}{4}}=\frac{2}{5}$