A random experiment has three possible outcomes A, B and C, with probabilities $p_A, p_B$ and $p_C$ What is the probability that, in independent performances of the experiment, A will occur before B?
Let an event D: A occurs before B
$ P(D) = _ + __ + __^2 + ⋯ = \frac{_}{1-p_c}$
I'm not able to get this solution. Why are there only events like $AC^n$, shouldn't it be like $A^mC^n$ where m and n denote the number of times event A or C is happening before B. Therefore shouldn't the sum should include terms like $p_a^mp_c^n$ ?