I am reading a probability text book and I am having difficulty understanding a paragraph and how the equation was setup. Can anyone please explain it in more detail or show me how this was derived? Please see the hyperlink to the screenshot.
"Equation 2-3" is the conditional probability P[A|B] = P[AB]/P[B]
What I think I understand:
- I understand the formula P[A] = pa + qB
- The first trial is a success, so I understand p^(s-1) term
I lose understanding at the Bth trial and anything after that, its probability q*p^(B-2), and conditional probability of A. The highlighted parts are what I am having trouble with.
Any help or clear way to understand will be appreciated very much.
Thank you
Textbook: The Theory of Gambling and Statistical Logic by Richard A. Epstein