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 has failed in Mathematics, is

• A. $\frac{1}{10}$
• B. $\frac{2}{5}$
• C. $\frac{9}{20}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

Let $A$ : the student fails in Physics and
$B$ : The student fails in Mathematics.
$\therefore P(A)=\frac{30}{100} $
$ P(B)=\frac{25}{100}$
and $ P(A \cap B)=\frac{10}{100}$
Now, $ P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}$
$-\frac{\frac{10}{100}}{\frac{25}{100}}=\frac{10}{100} \times \frac{100}{25}=\frac{10}{25}-\frac{2}{5}$