Question

A person goes to office by a car or scooter or bus or train, probability of which are $1/7,3/7.2/7$ and $1/7$ respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is $2/9,1/9,4/9$, and $1/9$ respectively. Given that he reached office in time, the probability that he travelled by a car is

• A. $1/7$
• B. $2/7$
• C. $3/7$
• D. $4/7$

Answer 1

The correct option is A $1/7$

Required probability $=\frac{\frac{1}{7}\times \frac{7}{9}}{\frac{1}{7}\times \frac{7}{9}+\frac{3}{7}\times \frac{8}{9}+\frac{2}{7}\times \frac{5}{9}+\frac{1}{7}\times \frac{8}{9}}=\frac{1}{7}$