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I was walking past a tree when I thought about a problem which I've been trying to solve.

It states that "If there are 20 leaves on a tree and all the leaves fall on the floor, find the probability that one leave will fall pointing directly north" . Does anyone have any ideas of how to attack this problem?

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    This is analogous to asking, "If I pick a real number between $0$ and $1$, what is the probability that I pick exactly $1/2$?"In general, if you have a continuous probability distribution over $\mathbb{R}$, the probability of any particular number is $0$ (although is is possible to have a probability measure with atoms, but then the cumulative distribution function isn't continuous).2011-05-24

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Unless you allow some tolerance around directly north, the chance is zero. If you allow a tolerance (plus or minus) of $\epsilon$ the chance for one leaf is $\frac{\epsilon}{\pi}$ and the chance of at least one of twenty is $1-\left(\frac{\pi-\epsilon}{\pi}\right)^{20}$. It's just like flipping a coin.

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    +1. Replace $\pi$ by 180 if you think in degrees rather than radians.2011-05-24