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Snowflakes are falling at an average rate of 10 flakes per square inch per minute. Calculate the probability that a 2 square-inch region has no snow flakes in a given 5 second time interval.

How should I know to use Poisson distribution in this case? What are the events to be modeled?

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We can model the situation by imagining $n$ snowflakes, with $n$ a million or more, each independently having probability $p$ of hitting our square inch bald patch, where $np=10$. In principle we have a binomial distribution. In practice, aince $n$ is very large and $np$ is modest, we can approximate the binomial distribution by using the Poisson. –  André Nicolas Oct 8 '12 at 21:02
    
Poisson approximates Binomial especially well if $p=\varphi(n)$,e.g. $p=\frac{1}{n}$, then $\lambda=np=1$ –  Alex Oct 9 '12 at 2:37

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Poisson PDF is $\frac{e^{-\lambda}{\lambda}^{k}}{k!}$ with $k=0, \lambda=10$. But in your case there are two more parameters: space and time, so the probability becomes $$ P(\textbf{ no flakes})=\left. \frac{e^{-\lambda t s}{(\lambda t s)}^{k}}{k!} \right|_{t=\frac{1}{12},\ s=2,\ k=0}=e^{-\frac{5}{3}} $$

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