GATE CE 2022 Set 1 — Question 63
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Engineering Mathematics → Probability → Poisson Distribution
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Question
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of vehicles per hour and vehicles per hour, respectively. The probability of observing at least vehicles in minutes is ______. (round off to two decimal places)
Correct answer
0.78 to 0.82
Solution
The arrival of cars and buses are independent Poisson processes. The combined arrival rate is the sum of the individual rates:
For a time interval , the mean number of arrivals is:
The probability of observing at least 2 vehicles is given by:
Using the Poisson probability mass function :
Rounding to two decimal places, the probability is .
For a time interval , the mean number of arrivals is:
The probability of observing at least 2 vehicles is given by:
Using the Poisson probability mass function :
Rounding to two decimal places, the probability is .
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