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Question

A person goes to office either by car, scooter, bus or train, the probability of which being 17, 37, 27 and 17 respectively. The probabilities that he reaches the office late, if he takes a car, scooter, bus or train are 29, 19, 49 and 19, respectively. Given that he reaches the office on time, then what is the probability that he travelled by car?

A
17
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B
27
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C
29
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D
421
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Solution

The correct option is A 17
As the statement shows problem is to be related to Bayes' theorem.
Let C, S, B, T be the events when person is going by car, scooter, bus or train, respectively.
P(C)=17, P(S)=37, P(B)=27, P(T)=17
Again, L be the event of the person reaching office late.
¯L be the event of the person reaching office in time.
Then, P(¯LC)=79, P(¯LS)=89, P(¯LB)=59
and P(¯LT)=89
P(CL)=P(¯LC).P(C)P(¯LC).P(C)+P(¯LS).P(S)+P(¯LB).P(B)+P(¯LT).P(T)
=79×1779×17+89×37+59×27+89×17=17

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