Question

A doctor has to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by 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, than he will not be late. When he arrives, he is late. What is the probability that he comes by train ?

Answer 1

Let E be the event “Doctor comes late to visit a patient” and if Doctor comes by Train, Bus, Scooter and any-other means, then probabilities are T₁, T₂, T₃ and T₄ respectively.

He does not late on coming by other means of transport.

Hence, using Baye's theorem.

Probability of late coming the doctor by train.

Hence, required probability = 1/2