Maybe I made it too complicated, so basically here is a simpler version
Just say two people toss a coin, with the geometric distributions of getting a head, respectively
Note: p1 != p2
What's probablity player 2 gets a head before player 1 does.
So say, player 2 gets a head at the 10th trial, then player 1 has to be 11.....n
Can anyone help me with this?