Shuttle bus which links the Clayton campus to the Caulfied campus starts operating at 5:00 am and will have a service every half hour. Suppose that none of the seats on the bus are completely occupied and that there is always some room for passengers. A student who wants to travel to Caulfied arrives at the bus stop at a (uniform) random time between 8:45 am and 9:45 am. What is the probability that he/she waits at most 10 minutes? Write down your answer to an accuracy of 2 decimal points.
Question
Shuttle bus which links the Clayton campus to the Caulfied campus starts operating at 5:00 am and will have a service every half hour. Suppose that none of the seats on the bus are completely occupied and that there is always some room for passengers. A student who wants to travel to Caulfied arrives at the bus stop at a (uniform) random time between 8:45 am and 9:45 am. What is the probability that he/she waits at most 10 minutes? Write down your answer to an accuracy of 2 decimal points.
Solution 1
The student arrives at a random time between 8:45 am and 9:45 am, which is a 60-minute window. The bus arrives every 30 minutes, so within this 60-minute window, there will be two bus arrivals.
The student wants to wait at most 10 minutes. This means that if the student arrives within 10 minutes before the bus arrives, he/she will wait at most 10 minutes. Since there are two bus arrivals within the 60-minute window, there are two 10-minute windows in which the student can arrive and wait at most 10 minutes.
Therefore, the total time in which the student can arrive and wait at most 10 minutes is 2 * 10 = 20 minutes.
The probability that the student waits at most 10 minutes is the ratio of the time in which the student can arrive and wait at most 10 minutes to the total time window:
Probability = (Time in which student can arrive and wait at most 10 minutes) / (Total time window) = (20 minutes) / (60 minutes) = 0.33 (rounded to two decimal places)
So, the probability that the student waits at most 10 minutes is approximately 0.33, or 33%.
Solution 2
The student arrives at a random time between 8:45 am and 9:45 am, which is a 60-minute window. The bus arrives every 30 minutes, so within this 60-minute window, there will be two bus arrivals.
The student wants to wait at most 10 minutes. This means that if the student arrives within 10 minutes before the bus arrival, he/she will wait at most 10 minutes. Since there are two bus arrivals within the 60-minute window, there are two 10-minute windows in which the student can arrive and wait at most 10 minutes.
Therefore, the probability that the student waits at most 10 minutes is the total time in which the student can arrive and wait at most 10 minutes divided by the total time window:
P(wait at most 10 minutes) = (10 minutes + 10 minutes) / 60 minutes = 20 / 60 = 0.33
So, the probability that the student waits at most 10 minutes is approximately 0.33, or 33%, to an accuracy of 2 decimal points.
Similar Questions
Tom often waits for the 192 bus at the University of Queensland's Lake Bus Station, where he has noticed that it departs from the Lake Bus at a rate of six buses per hour. What is the probability that he will be able to wait for one bus in a 1-minute period (round your answer to four decimal places)?
The number of minutes that Samantha waits to catch the bus is uniformly distributed between 0 and 15 minutes. What is the probability that Samantha has to wait less than 4.5 minutes to catch the bus?
Riya leaves for school between 7:00 AM and 7:15 AM. She takes between 20 and 30 minutes to reach the school. Let 𝑋X denote her time of departure, and let 𝑌Y denote her travel time. Assuming that 𝑋X and 𝑌Y are continuous, independent and uniformly distributed, find the probability that she reaches the school before 7:30 AM. Enter the answer correct to two decimal places.
Students arrive at Central Library at an average of 15 per quarter of the lunch hour. What is the probability that the next student will arrive within 5 minutes? ( round your answer to four decimal places)
Jason goes to school either by bus or on foot. If he gets up late in the morning, the probability that he goes by bus is 4/5. If he does not get up late in the morning, the probability that he goes by bus is 1/10. If the probability that he gets up late in morning is 1/20, find the probability that Jason goes to school on foot in a school day.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.