Probability of Falling leaves 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?

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.