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 $E_1$ be the event that a student fails in physics and $E_2$ be the event that a student fails in mathematics.
$\therefore P\left(E_{1}\right)= \frac{30}{100} = \frac{3}{10}$,
$P\left(E_{2}\right) = \frac{25}{100} = \frac{1}{4}$
$P\left(E_{1} \cap E_{2}\right) = \frac{10}{100} = \frac{1}{10}$
$\therefore $ Required probability $= P\left(E_{1} | E_{2}\right) = \frac{P\left(E_{1} \cap E_{2}\right)}{P\left(E_{2}\right)}$
$= \frac{1/10}{1/4} = \frac{4}{10} = \frac{2}{5}$