Finding the probability that $A$ occurs before $B$ Given an experiment has $3$ possible outcomes $A, B$ and $C$ with respective probabilities $p, q$ and $r$ where $p + q + r = 1.$ The experiment is repeated until either outcome $A$ or outcome $B$ occurs. How can I show that $A$ occurs before B with probability $\dfrac{p}{p+q}$?

The occurrences of $C$ are irrelevant in deciding whether $A$ comes before $B$ or vice versa,
hence the desired $Pr = \frac p{p+q}$
