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 given by

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

The correct option is A $\frac{1}{2}$

Probability of students fails in English $=P\left(E\right)=30\%=\frac{30}{100}$

Probability of students fails in Hindi $=P\left(H\right)=20\%=\frac{20}{100}$

Probability of students fails in English and Hindi both $=P(E\cap H)=10\%=\frac{10}{100}$

Probability of students fails in English given fails in Hindi,

$P\left(E/H\right)=\frac{P(E\cap H)}{P\left(H\right)}=\frac{10/100}{20/100}=\frac{1}{2}$