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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.

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.

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
10 years ago
Hello Student,
P(C)=1/7
P(S)=3/7
P(B)=2/7
P(T)=1/7
I be the event of him reaching in time.
P(I/C)=7/9
P(I/S)=8/9
P(I/B)=5/9
P(I/T)=8/9
=>P(C/I)=P(I/C)P(C)/P(I)=1/7*7/9/(1/7*7/9+3/7*8/9+2/7*5/9+8/9*1/7)=1/7

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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