The probabilities that a government servant goes to work by car, bus or train on a certain day are 1/10, 2/5 and 1/2 respectively. The probabilities of his being late for work by these modes of transport are 1/5,1/2 and 3/10 respectively. If he was late on this particular day, using Bayes’ Theorem, calculate the probability that he travelled be train.
Let define a notation to answer this question.
P(C)=probability traveled by car
P(B) = probability travelled by Bus
P(T)= probabilty travelled by train
P(L/C)=prabability being late travelled by car
and similarly we can define P(L/B) and P(L/T).
Thus by Bayes Theorem
`` Hence he was late on this particular day, the probability that he travelled be train is 15/37.