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Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D? 

  • a)
    9/128   

  • b)
    13/64  

  • c)
    119/128  

  • d)
    8/13  

Correct answer is option 'A'. Can you explain this answer?
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Solution:

Total waiting time allowed = 13 minutes
Maximum waiting time at each stop = 8 minutes
Probability of waiting time up to 8 minutes at each stop = 1/2

To arrive on time, the total waiting time should be less than or equal to 13 minutes.

Let's consider different cases of waiting times at stop B and stop C:

Case 1: No waiting time at B or C
In this case, Manish will spend zero waiting time at both stops. Hence, the total waiting time will be zero and he will arrive on time at D. Probability of this case = 1/4.

Case 2: Waiting time of 8 minutes at one stop and no waiting time at the other stop
In this case, Manish will spend 8 minutes waiting time at one stop and zero waiting time at the other stop. Hence, the total waiting time will be 8 minutes and he will arrive on time at D. Probability of this case = 2 x (1/2) x (1/4) = 1/4.

Case 3: Waiting time of 8 minutes at both stops
In this case, Manish will spend 8 minutes waiting time at both stops. Hence, the total waiting time will be 16 minutes and he will arrive late at D. Probability of this case = (1/2) x (1/2) = 1/4.

Case 4: Waiting time of less than 8 minutes at both stops
In this case, Manish will spend some waiting time at both stops, but the total waiting time will be less than 13 minutes. Hence, he will arrive on time at D. Probability of this case = 1 - (1/4) - (1/4) - (1/4) = 1/4.

Therefore, the probability of Manish arriving late at D = probability of Case 3 = 1/4.

Hence, the correct answer is option A) 8/13.
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Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D?a)9/128 b)13/64 c)119/128 d)8/13 Correct answer is option 'A'. Can you explain this answer?
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Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D?a)9/128 b)13/64 c)119/128 d)8/13 Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D?a)9/128 b)13/64 c)119/128 d)8/13 Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D?a)9/128 b)13/64 c)119/128 d)8/13 Correct answer is option 'A'. Can you explain this answer?.
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