A person goes to office either by car, scooter, bus or train probability of which being`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, then what is the probability that he travelled by a car?

Options

A. `1/5`
B. `1/7`
C. `6/7`
D. None of these

Answer

2

Explanation

Let C, S, B, T be the events that the person reaching the office in time -
`P(C )=1/7,P(S)=3/7,P(B)=2/7,(T)=1/7`
Let `barL` be the event that the person reaching the office in time -
`P(barL//C)=7/9,P(barL//S)=8/9,`
`(x-1)/(9)=(y-2)/(-1)=(z+3)/(-3)`
`thereforeP(C//barL)=(P(C)P(barL//C))/(P(barL))`
`=(1/7cdot7/9)/(1/7cdot7/9+3/7cdot8/9+2/7cdot5/9+1/7cdot8/9)`
`=7/49=1/7`