Probability 1

Panel 1: The mathematician: Did you know that even events with probability 1 are not guaranteed to happen? Man: …no, this is a bad idea and you should write your comic about something else. Panel 2: Speeck balloon: Hey, do you remember $ 1-\left(2^{(-n)} +\sum_{k=1}^{n-2} \left( \left( \frac{\left(n-1\right)!} {k!\left(n-k-2\right)!} \right) \int_{x=\frac{1}{2}}^1 (x-\frac{1}{2})^k(1-x)^{(n-k-2)}dx \right) \right)$? It turns out that it's $1+3\left(\frac{1}{2}\right)^n-\left(\frac{1}{2}\right)^n n$ instead of $1-\left(\frac{1}{2}\right)^n n$. Speech balloon: Oops, I must have meant $ 1-\left(2^{(2-n)} +\sum_{k=1}^{n-2} \left( \left( \frac{\left(n-1\right)!} {k!\left(n-k-2\right)!} \right) \int_{x=\frac{1}{2}}^1 (x-\frac{1}{2})^k(1-x)^{(n-k-2)}dx \right) \right)$ or $ 1-\left(2^{(1-n)} +\sum_{k=1}^{n-2} \left( \left( \frac{\left(n-1\right)!} {k!\left(n-k-2\right)!} \right) \int_{x=\frac{1}{2}}^1 (x-\frac{1}{2})^k(1-x)^{(n-k-2)}dx \right) \right)$.

This is a response to a mathematical formula in another author's Tech comic. Sadly I believe I still screwed up my ammendmended formula.

Probability 1

9 March 2007