The main line train starts at 5:00 am and harbor line train starts at 5:02 am.…
2025
The main line train starts at 5:00 am and harbor line train starts at 5:02 am. Each train has a frequency of 10 minutes. If a man goes in the morning at a random time, What is the probability that he will get the main line train ?
- A.
1/5
- B.
1/4
- C.
4/5
- D.
1/2
Attempted by 13 students.
Show answer & explanation
Correct answer: C
Answer: 4/5
Reasoning:
Look at any 10-minute interval starting when a main-line train departs (for example, from 5:00 to 5:10).
The main-line train departs at the start of the interval (time 0). The harbor-line train departs 2 minutes later (time 2) because it starts at 5:02 and also repeats every 10 minutes.
If a person arrives uniformly at random during this interval, arriving between time 0 and 2 minutes means the next train is the harbor-line; arriving between time 2 and 10 minutes means the next train is the main-line.
Therefore the main-line is the next train for 8 minutes out of every 10, so the probability is 8/10 = 4/5.