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Question

A person goes to work by car, train or bus. The probabilities of person travelling by there modes are 3/10,1/2 and 1/5 respectively. It is found that chance of person being late for work are 3/7,1/7 and 5/7 by respective modes. Given that on particular day person reaches late, find the probability that on that day he had travelled by train.

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Solution

UsingBayesRuleProbabilitythathetravelledbytraingivenheislate=ProbabilityheislateandusedtrainProbabilitythatheislatebyothermodeoftransport=(1/2)×(1/7)(3/10)×(3/7)+(1/2)×(1/7)+(1/5)×(5/7)=524

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