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A volcano erupts 10 times in 200 years. What is the probability that it will erupt next year?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A volcano erupts 10 times in 200 years. What is the probability that it will erupt next year?

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Expert Solution

Step 1

Poisson Distribution:

If the average probability of an event happening per unit, and there is a need to find the probability of the certain number of events that are happening in a period, the Poisson distribution is used.

If the mean number of successes is $μ$ and $x$ is the actual number of successes, the probability of Poisson distribution is calculated as follows:

$P (x; μ) = \frac{e^{- μ} μ^{x}}{x!}$

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