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A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, and scooter or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are 1/4 , 1/3 and 1/12, 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 is late. The probability that he comes by bus is:​
  • a)
    1/6
  • b)
    4/9
  • c)
    5/18
  • d)
    1/18
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A doctor is to visit a patient. From the past experience, it is known ...
The correct answer is B.
Let T1:Event that doctor came by train
T2:Event that doctor came by Bus
T3:Event that doctor came by scooter
T4:Event that doctor came by other means of transport
L :Event that doctor arrives late.
Probability if doctor comes by train if he is late
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Most Upvoted Answer
A doctor is to visit a patient. From the past experience, it is known ...
Given Information:
- The probabilities of the doctor coming by train, bus, scooter, or other means of transport are 0.3, 0.2, 0.1, and 0.4 respectively.
- The probabilities of the doctor being late if he comes by train, bus, and scooter are 1/4, 1/3, and 1/12 respectively.
- If the doctor comes by other means of transport, he will not be late.

Required:
The probability that the doctor comes by bus given that he arrives late.

Solution:
Let's calculate the probability of the doctor arriving late:

P(Late) = P(Late | Train) * P(Train) + P(Late | Bus) * P(Bus) + P(Late | Scooter) * P(Scooter) + P(Late | Other) * P(Other)

Given:
P(Late | Train) = 1/4
P(Late | Bus) = 1/3
P(Late | Scooter) = 1/12
P(Late | Other) = 0 (as he will not be late if he comes by other means of transport)

Substituting these values in the equation, we get:

P(Late) = (1/4) * (0.3) + (1/3) * (0.2) + (1/12) * (0.1) + 0 * (0.4)
= 0.075 + 0.0667 + 0.0083 + 0
= 0.15

Now, let's calculate the probability that the doctor comes by bus given that he arrives late:

P(Bus | Late) = (P(Late | Bus) * P(Bus)) / P(Late)

Substituting the given values and calculated probability of being late, we have:

P(Bus | Late) = (1/3) * (0.2) / 0.15
= 0.0667 / 0.15
= 4/9

Therefore, the probability that the doctor comes by bus given that he arrives late is 4/9. Hence, the correct answer is option B.
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A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, and scooter or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are 1/4 , 1/3 and 1/12, 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 is late. The probability that he comes by bus is:​a)1/6b)4/9c)5/18d)1/18Correct answer is option 'B'. Can you explain this answer?
Question Description
A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, and scooter or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are 1/4 , 1/3 and 1/12, 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 is late. The probability that he comes by bus is:​a)1/6b)4/9c)5/18d)1/18Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, and scooter or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are 1/4 , 1/3 and 1/12, 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 is late. The probability that he comes by bus is:​a)1/6b)4/9c)5/18d)1/18Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, and scooter or by other means of transport are respectively 0.3, 0.2, 0.1 and 0.4. The probabilities that he will be late are 1/4 , 1/3 and 1/12, 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 is late. The probability that he comes by bus is:​a)1/6b)4/9c)5/18d)1/18Correct answer is option 'B'. Can you explain this answer?.
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