12. Let and F be mutually exclusive events in the sample space of an experiment. Suppose...

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

Hint: Argue that the probability that the original experiment is performed ç times and Å appears on the nth time is P(E) x (1 - p)n~l 9

« = 1,2,..., where ñ = P(E) + P(F). Add these probabilities to get the desired answer.