Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > At a traffic intersection, cars and buses arr...
Start Learning for Free
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)
Correct answer is between '0.78,0.82'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
At a traffic intersection, cars and buses arrive randomly according to...
Solution:
Given:
- Cars arrive randomly according to Poisson process with an average rate of 4 vehicles per hour.
- Buses arrive randomly according to Poisson process with an average rate of 2 vehicles per hour.
- We need to find the probability of observing at least 2 vehicles in 30 minutes.
Finding the probability of at least 2 vehicles in 30 minutes:
- Let X denote the number of cars arriving in 30 minutes.
- Let Y denote the number of buses arriving in 30 minutes.
- X and Y are independent Poisson random variables.
- The average rate of cars arriving in 30 minutes is 2 (since 30 minutes = 0.5 hours).
- The average rate of buses arriving in 30 minutes is 1 (since 30 minutes = 0.5 hours).
- The probability of observing at least 2 vehicles in 30 minutes can be calculated as follows:
P(X+Y ≥ 2) = 1 - P(X+Y = 0) - P(X+Y = 1)
- P(X+Y = 0) can be calculated as follows:
P(X+Y = 0) = P(X = 0) × P(Y = 0)
= e^-2 × e^-1
= e^-3
- P(X+Y = 1) can be calculated as follows:
P(X+Y = 1) = P(X = 0) × P(Y = 1) + P(X = 1) × P(Y = 0)
= e^-2 × 2e^-1 + 4e^-2 × e^-1
= 6e^-4
- Therefore, the probability of observing at least 2 vehicles in 30 minutes is:
P(X+Y ≥ 2) = 1 - e^-3 - 6e^-4
= 0.7988 (rounded off to two decimal places)
Therefore, the correct answer is between 0.78 and 0.82, which includes the calculated probability of 0.7988.
Given:
- Cars arrive randomly according to Poisson process with an average rate of 4 vehicles per hour.
- Buses arrive randomly according to Poisson process with an average rate of 2 vehicles per hour.
- We need to find the probability of observing at least 2 vehicles in 30 minutes.
Finding the probability of at least 2 vehicles in 30 minutes:
- Let X denote the number of cars arriving in 30 minutes.
- Let Y denote the number of buses arriving in 30 minutes.
- X and Y are independent Poisson random variables.
- The average rate of cars arriving in 30 minutes is 2 (since 30 minutes = 0.5 hours).
- The average rate of buses arriving in 30 minutes is 1 (since 30 minutes = 0.5 hours).
- The probability of observing at least 2 vehicles in 30 minutes can be calculated as follows:
P(X+Y ≥ 2) = 1 - P(X+Y = 0) - P(X+Y = 1)
- P(X+Y = 0) can be calculated as follows:
P(X+Y = 0) = P(X = 0) × P(Y = 0)
= e^-2 × e^-1
= e^-3
- P(X+Y = 1) can be calculated as follows:
P(X+Y = 1) = P(X = 0) × P(Y = 1) + P(X = 1) × P(Y = 0)
= e^-2 × 2e^-1 + 4e^-2 × e^-1
= 6e^-4
- Therefore, the probability of observing at least 2 vehicles in 30 minutes is:
P(X+Y ≥ 2) = 1 - e^-3 - 6e^-4
= 0.7988 (rounded off to two decimal places)
Therefore, the correct answer is between 0.78 and 0.82, which includes the calculated probability of 0.7988.
Free Test
FREE
| Start Free Test |
Community Answer
At a traffic intersection, cars and buses arrive randomly according to...
λC = 4 Vehicle/hr = 2 Vehicle/30 min
λB = 2 Vehicle/hr = 1 Vehicle/30 min
λvehicle = 3 Vehicle/30 min
P(x < 2) = 1 - P(x ≤ 1)
= 1 - [P(x = 0) + P(x = 1)1
λB = 2 Vehicle/hr = 1 Vehicle/30 min
λvehicle = 3 Vehicle/30 min
P(x < 2) = 1 - P(x ≤ 1)
= 1 - [P(x = 0) + P(x = 1)1
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer?
Question Description
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer?.
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer?.
Solutions for At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer?, a detailed solution for At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? has been provided alongside types of At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is _____ . (round off to two decimal places)Correct answer is between '0.78,0.82'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup