If $n$ flips are required to get $r$ heads, it means in $n-1$ flips you already have $r-1$ heads and the $n^{th}$ flip is a head. Assuming successive flips are independent,

$P(X=n)=P(r-1 \text{ heads in } n-1 \text{ flips})*p$

$P(X=n)=\binom{n-1}{r-1}p^{r-1}{(1-p)}^{n-r}*p$

Probability...coin toss
Vs. a normal midi keyboard and the Midi Pro adapter?  In particular,


The RB3 Keyboard is not a full-sized keyboard.  If we do use a full-sized midi keyboard in Pro mode, can we/do we have to use the entire keyboard, as it's played in the actual song, or can we/do we have to stick to two octaves (like the RB3 Keyboard)?
The RB3 Keyboard can also function as a five-button peripheral in non-Pro mode.  Can we do the same with a normal midi keyboard?
I've read that the RB3 keyboard has velocity-sensitive keys.  Does RB3 take this into effect?  Will I lose some functionality if my midi keyboard isn't velocity-sensitive?  Does the expressions bar also add functionality?

