Problem # 6. Consider a repeated experiment and two events A and B. a) Let A and B be mutually exclusive events with probabilities pa and pb, respectively. Independent trials of the experiment are performed to see which one of the two occurs first. What is the probability that event A occurs before event B? b) Next solve a similar problem for the case where A and B are independent events (and not mutually exclusive). What is the probability that B does not occur before A? (Note that now we must allow for the possibility that they occur simultaneously).