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A person goes to his office by using dif...

A person goes to his office by using different means of transport on different days. It is know that the probabilities that he will come by train, bus, scooter or by car are respectively `1/10, 3/10, 2/10 " and " 4/10`. The probabilities that he will be late are `1/4, 1/5, 1/6, " and " 1/3` if he comes by train, bus, scooter and car respectively, on one day when he reaches office, he is late. What is the probability he has come by train?

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AI Generated Solution

To solve the problem, we will use Bayes' theorem. We need to find the probability that the person came by train given that he is late. ### Step-by-Step Solution: 1. **Define Events:** - Let \( E_1 \): The event that the person comes by train. - Let \( E_2 \): The event that the person comes by bus. - Let \( E_3 \): The event that the person comes by scooter. ...
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