A Probability Problem

I realize it's summer for De Anza students, and the last thing you want to do is a probability problem, but I couldn't resist....

This post is for those of you who know some basic probability. For those of you who don't, feel free to email me (jefferson_deanza@yahoo.com) for an explanation.

I went through a scoring drought (that was broken this evening, when I scored a controversial) on my soccer team. I hadn't scored in 5 straight games. I began to think about how my scoring in a soccer game affects the team's winning or losing that game.

I will let W = a game the team wins and S = me scoring at least one goal in a game.

Over the past 14 games (spring season, a friendly game, and 3 games into the summer season), the team has won 8 of 14 games, and I have scored a goal in 5 of 14 games.

The probability of winning is P(W) = 8/14 and the probability of me scoring is P(S) = 5/14. The probability of winning or of me scoring is P(W or S) = 8/14. Given this information, what is the probability of the team winning, given that I score a goal: P(W | S) = ??

The answer is kind of cool, I think.