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