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GATE 2024 CE (CE1) – Question 47

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

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson's distribution, the probability that it will be exceeded at least once in 50 years is ________________ % (rounded off to the nearest integer).

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Correct answer: 22

Explanation

The mean number of events in 50 years is $\lambda = \frac{50}{200} = 0.25$. The probability of at least one is $1 - e^{-0.25} = 1 - 0.7788 = 0.2212$, which is 22%.