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GATE 2021 CE (CE1) – Question 47

Engineering Mathematics · Probability and Statistics: Random variables, Poisson and Normal distributions, linear regression · 2 marks · Numerical answer

Vehicular arrivals follow a Poisson process with mean rate 2 vehicles/min. Find probability of at least two arrivals in one minute, to two decimals.

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Correct answer: .58 to .60

Explanation

For X~Poisson(2), $P(X\ge2)=1-P(X=0)-P(X=1)=1-e^{-2}-2e^{-2}=0.593994$. Rounded to two decimals, the probability is **0.59**. “At least two” includes two, so only counts zero and one are excluded.