Introduction to Probability · Problem 5.1.27
Distributions and Densities — Grinstead & Snell
Mathematics — Probability · poisson-distribution
Problem
Assume that the probability that there is a significant accident in a nuclear power plant during one year's time is .001. If a country has 100 nuclear plants, estimate the probability that there is at least one such accident during a given year.Intuitive explanation
This is a rare-event probability problem where you need to find "at least one" success. The key insight is to use the complement rule: it's much easier to calculate the probability that nothing happens, then subtract from 1. Since each plant has a tiny accident probability, the probability all 100 plants stay safe is , and flipping that gives you your answer.
Intuitive explanation
This is a rare-event probability problem where you need to find "at least one" success. The key insight is to use the complement rule: it's much easier to calculate the probability that nothing happens, then subtract from 1. Since each plant has a tiny accident probability, the probability all 100 plants stay safe is , and flipping that gives you your answer.