GATE 2022 CE (CE1) – Question 63
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)
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Correct answer: 0.79 to 0.81
Explanation
Independent Poisson arrival streams add, giving a combined rate 4+2=6 vehicles/h. Over half an hour the mean is λ=3.
Thus $P(N\ge2)=1-P(0)-P(1)=1-e^{-3}(1+3)=0.8008517$. **Answer: 0.80**.