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 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

Explanation

To find the probability that the doctor comes by train given that he is late, we can use Bayes' theorem. Let's denote the events as follows:

- Let \( T_1 \): the event that the doctor comes by train.
- Let \( T_2 \): the event that the doctor comes by bus.
- Let \( T_3 \): the event that the doctor comes by scooter.
- Let \( T_4 \): the event that the doctor comes by other means of transport.
- Let \( E \): the event that the doctor is late.

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