Question

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

• A. 3/7
• B. 1/7
• C. 6/7
• D. 5/7

Answer 1

The correct option is B

1/7

Let C,S,B and T be the events associated with the travelling.

P(C)=$\frac{1}{7}$

P(T)= $\frac{3}{7}$

P(B)= $\frac{2}{7}$

P(S)= $\frac{1}{7}$

P(L’)=Probability that the person reaches on time

P$\left(\frac{L^{\prime }}{C}\right)=\frac{7}{9}$

P$\left(\frac{L^{\prime }}{T}\right)=\frac{8}{9}$

P$\left(\frac{L^{\prime }}{B}\right)=\frac{5}{9}$

P$\left(\frac{L^{\prime }}{S}\right)=\frac{8}{9}$

P$\left(\frac{C}{L}\right)=P\left(\frac{L^{\prime }}{C}\right)\times P\left(\frac{C}{L^{\prime }}\right)=(\frac{1}{7}\times \frac{7}{9})+(\frac{3}{7}\times \frac{8}{9})+(\frac{2}{7}\times \frac{5}{9})+(\frac{8}{9}\times \frac{1}{7})=\frac{1}{7}$