Probability of Winning in Sports In sports such as volleyball (prior to 1999), you can score a point only if it is your turn, with turns alternating until a point is scored. Suppose your probability of scoring a point when it is your turn is $p$, and your opponent's probability of scoring a point when it is her turn is $q$. Find a formula for the probability $S$ that you are the first to score the next point, assuming it is currently your turn.
I have little experience with probability problems, so any help would be well appreciated!

Assume the probability of you scoring the next point if it is your turn now is $x$. 
The probability is p that you score immediately. The probability is $(1-p)(1-q)$ that you don't score, then your opponent doesn't score, and it's your turn again to win with probability $x$. 
So $x = p + (1-p)(1-q) x$, and you calculate $x$ from that getting $x  = \frac p{ p + q - pq}$
