Comprehension
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Question 2 /9
Nobita’s two friends Giyan and Sunio want to see him every weekend, but they live on opposite sides of town. As a compromise, he tells them that every Sunday, he’ll head to the subway station nearest to his apartment at a random time of the day and will hop on the next train that arrives.
If it happens to be the train traveling north, he’ll visit his friend Giyan uptown, and if it happens to be the train traveling south, he’ll visit his friend Sunio downtown. Both of his friends are okay with this plan, since they know both the northbound and southbound trains run every 20 minutes.
But after a few months of doing this, Sunio complains that he sees Nobita only one out of five Sundays. Nobita promises he’s indeed heading to the station at a random time each day.
Based on the above information answer questions given below:-
What should be the difference in arrival time of the trains so that the probability of either train will be ½.
Answers
Given : northbound and Southbound train run every 20 minutes
If it happens to be the train travelling North, he will visit his friend Giyan uptown, and if it happens to be the train travelling South, he will visit his friend sunio downtown
Sunio Complains that he sees Nobita only one out of five Sundays.
To Find : the difference in arrival of both the trains?
What should be the difference in arrival time of the trains so that the probability of either train will be ½.
Solution:
Let say difference between arrival of trains = x minutes
Southbound train comes after x minutes of Northbound train
as train run every 20 minutes
Northbound train train comes after Southbound train in 20 - x minutes
Probability of catching the Southbound train which comes after x minutes = x/20
he sees Nobita only one out of five Sundays = 1/5
=> x/20 = 1/5
=> x = 4
Southbound train comes after 4 minutes of Northbound train
and Northbound train comes after 16 minutes of southbound train
difference in arrival time of the trains so that the probability of either train will be ½.
=> x /20 = 1/2 => x = 10
20 - x = 10
Southbound train comes after 10 minutes of Northbound train
and Northbound train comes after 10 minutes of southbound train
difference in arrival time of the trains should be 10 minutes so that the probability of either train will be ½.
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