$\begin{array}{1 1} (A)\;\large\frac{1}{10}\quad(B)\;\large\frac{2}{5}\quad (C)\;\large\frac{9}{20}\quad(D)\;\;\large\frac{1}{3}\end{array} $

- If $E$ and $F$ are two events associated with sample space.
- The conditional probability of event $E$ under the condition that event $F$ has occured is given by
- $p(E/F)=\Large\frac{p(E\cap F)}{p(F)}$
- $p(F)\neq 0$

p(student fails in Physics)=p(E)$=30\%=\large\frac{30}{100}$

p(student fails in Mathematics)=p(F)$=25\%=\large\frac{25}{100}$

p(fails both in Physics and Mathematics)$=p(E\cap F)=10\%=\large\frac{10}{100}$

p(Fails in Physics given tails in Mathmatics)

$p(E/F)=\Large\frac{p(E\cap F)}{p(F)}$

=$\Large\frac{10/100}{25/100}$

=$\Large\frac{2}{5}$

$'B'$ option is correct

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