A doctor is to visit a patient.
The probabilities that he comes by train, bus, scooter or other means are
\(\frac{3}{10}, \frac{1}{5}, \frac{1}{10}\) and \(\frac{2}{5}\) respectively.
The probabilities that he will be late are
\(\frac{1}{4}\) if he comes by train,
\(\frac{1}{3}\) if he comes by bus,
\(\frac{1}{12}\) if he comes by scooter.
If he comes by other means of transport, he will not be late.
When he arrives, he arrives late.
The probability that he comes by bus is:

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.