Brain Teaser - Do you understand conditional probability?

Probability may be the area of math that people most often make mistakes in. I knew a programmer who was convinced that because he set a limit to his casino losses on a given day that he was guaranteed to eventually come out ahead.

Many difficulties arise from a misunderstanding of conditional probability. Here is a very basic problem. See if you can come up with the correct solution.

A casino has two slot machines that are identical except that one is set to make payoffs 20% of the time and the other pays off 30% of the time. You randomly choose a machine and on the first pull you win. What is the probability that you chose the 30% payoff machine?