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A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by any other means of transport are respectively (3/10),(1/5), (1/10)and(2/5) . The probabilities that he will be late are (1/4), (1/3) and(1/12) if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by train.

SHAIK AASIF AHAMED
7 years ago
by applying bayes theorem we get
let l= probability of late
t=probability of late by train
P(t/l)= $\frac{(1/4)(3/10)}{(1/4)(3/10)+(1/3)(3/5)+(1/10)(1/12)}$
on simplification we get p(t/l)=1/2
Thanks & Regards
Jitender Singh
IIT Delhi