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 P(E)/

[P(E) + P(F)].

Hint: Argue that the probability that the original experiment is performed n times and E appears on the nth time is P(E)×(1−p)n−1, n = 1, 2,... , where p = P(E) + P(F). Add these probabilities to get the desired answer.