We discuss the probability based on the color of ball you first picked up. Then you continue to pick up the same color for totally $k-1$ time until you pick up another color at $k$th.

$E(X)=\sum\limits_{k=2}^\infty k[(\frac{1}{2})^{k-1}\frac{1}{2}+(\frac{2}{6})^{k-1}\frac{4}{6}+(\frac{1}{6})^{k-1}\frac{5}{6}]$

To calculate the sum, the easiest way is to make use of the fact:  for $|r|&lt;1$, $\sum\limits_{k=0}^\infty r^k=\frac{1}{1-r}$. Differentiate both sides, $\sum\limits_{k=1}^\infty kr^{k-1}=\frac{1}{(1-r)^2}$. Then $\sum\limits_{k=2}^\infty kr^{k-1}=\frac{1}{(1-r)^2}-1$

Expectation of drawing the second color from an urn
[Turns out this is known bug #9536151]

I have a strange issue with Quicklook in Lion. This is on a clean install and happens with  more than one user. It also isn't fixed if I clean out the Quicklook cache in /var/folders

I have to push the spacebar twice to get Quicklook to work properly. 

The first time the usual Quicklook 'window' appears but it is blank:



Push the spacebar again and the image appears. If I restart the Finder the problem goes away briefly. It's driving me nuts.
