Probability 4 Question 17

17. A person goes to office either by car, scooter, bus or train probability of which being 17,37,27 and 17, respectively. Probability that he reaches offices late, if he takes car, scooter, bus or train is 29,19,49 and 19, respectively. Given that he reached office in time, then what is the probability that he travelled by a car?

(2005, 2M)

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Answer:

Correct Answer: 17. 17

Solution:

  1. As, the statement shows problem is to be related to Baye’s law.

Let C,S,B,T be the events when person is going by car, scooter, bus or train, respectively.

P(C)=17,P(S)=37,P(B)=27,P(T)=17

Again, L be the event of the person reaching office late.

L¯ be the event of the person reaching office in time.

Then, PL¯C=79,PL¯S=89,PL¯B=59

and PL¯T=89

PCL=PL¯CP(C)PL¯CP(C)+PL¯SP(S)+PL¯BP(B)+PL¯TP(T)=79×1779×17+89×37+59×27+89×17=17



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