12. Let E and F be mutually exclusive events in the sample space of an experiment. Suppose that the experiment is repeated until either event E or event F occurs. What does the sample space of this new super experiment look like? Show that the probability that event E occurs before event F is .

Hint: Argue that the probability that the original experiment is performed n times and E appears on the nth time is

, where . Add these probabilities to get the desired answer.