By Bayes' theorem, P(late)=(3/10)(1/4)+(1/5)(1/3)+(1/10)(1/12)+(2/5)(0). Common denominator 120: 9/120+8/120+1/120=18/120=3/20. Then P(bus∣late)=[(1/5)(1/3)]/(3/20)=(1/15)(20/3)=4/9.
A doctor is to visit a patient. It is known that the probabilities that he will come by train, bus, scooter or by other means of transport are respectively 103,51,101 and 52. The probabilities that he will be late are 41,31 and 121, 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 arrives late.
The probability that he comes by bus is:
Held on 23 May 2023 · Verified 13 Jul 2026.
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