Question

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

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{4}{7}$

Answer 1

The correct option is A $\frac{1}{7}$

By Bayes' theorem of probability,
the probability that he travelled by a car is,
$=\frac{\frac{1}{7}\times \frac{7}{9}}{\frac{1}{7}\times \frac{7}{9}+\frac{3}{7}\times \frac{8}{9}+\frac{2}{7}\times \frac{5}{9}+\frac{1}{7}\times \frac{8}{9}}$

$=\frac{1}{7}$