# Why can't this be solved by binomial

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.

Problem is from Grinstead and Snell. They have solved by Poisson approximation. My question is why can't this be solved by binomial. To me it looks like a straight-forward binomial problem.

It can be solved, but the essence of approximations like Poisson or Normal is to get rid of large factorials and powers.

• Thank you. But I get a different answer from the book. My answer is close to 0.64. What are you getting?
– user218970
Sep 9, 2018 at 10:55
• @user585380 I'm getting 0.095 using an exact calculation (assuming independence). Is that (close to) what the book says? Sep 9, 2018 at 11:03
• @Dougal Yes, that's correct. How did you do it?
– user218970
Sep 9, 2018 at 11:08

(Answering assuming this is self-study; you should read the tag description there and add it to your question if appropriate.)

The easiest way to solve this kind of problem is usually to first answer the opposite. Instead of saying "what's the probability of 1 accident, or 2, or ...", you can say "what's the probability of 0 accidents", and then get the answer you want from there.

• Got the answer. The silly mistake that I made was to calculate probability as '0.01'. Missed an extra zero, therefore got the wrong answer all along
– user218970
Sep 9, 2018 at 11:14
• On another note, do you know of any books or resources to practice binomial and poisson problems of this level or slightly higher?
– user218970
Sep 9, 2018 at 11:15