Question

In a class $30$% students fail in English; $20$% students fail in Hindi and $10$% students fail in English and Hindi both. A student is chosen at random, then the probability that he will fail English if he has failed in Hindi is $\frac{k}{2}$.The value of $k$ is

Answer 1

Event of failing in English is denoted by 'E' and for Hindi it is denoted by 'H'.
Conditional probability states that $P\left(\frac{E}{H}\right)=\frac{P(E\cap H)}{P\left(H\right)}=\frac{0.1}{0.2}=\frac{1}{2}$
Hence,$k=1$