A person goes to office either by car, jeep, bus or train. The probabilities of which being 2/7, 3/7

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28 Apr 2011 probability

A person goes to office either by car, jeep, bus or train. The probabilities of which being 2/7, 3/7, 1/7 ,1/7 respectively. The probability that he reaches office later if he takes jeep, bus, car or train is 2/9, 1/9, 5/9, 2/9 respectively. If he reaches office in time, then the probability that he travelled by car is

OPtion

1) 2/7
2) 2/11
3) 4/13
4) 4/15
5) 7/19
6) 8/21
7) 9/19
8) 10/21
9) 11/32
10) 12/31

Solution

the probability that he travelled by car is 2/7
The probability that he reaches office later if he takes car is 5/9
So probability that he reaches office in time by car =(2/7)*(4/9)= 8/63
Similarly probability for jeep = (3/7)*(7/9) = 21/63
Similarly probability for bus = (1/7)*(8/9) = 8/63
Similarly probability for train = (1/7)*(7/9) = 7/63
so required probability = (8/63)/(8/63)+(21/63)+(8/63)+(7/63)= 8/44 = 2/11

Correct Option: 2 Best Solution (0)