A discrete mathematics problem by yogesh wankhade

Discrete Mathematics Level pending

A doctor is to visit a patient .From the past experience ,it is known that the probability of his coming by train, or by scooter or by other means are 3/10,1/5 and 2/5. The probabilities that he will be late when he comes by train , bus or scooter are 1/4 ,1/3 and 1/12 respectively. when he arrives , he is late .what is the probability that he comes by train ? what is the sum of numerator and denominator?

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