Let 0 < p < 1 and 0 < r < 1 with p ≠ r. You repeat a trial with success probability p until you see the first success. I repeat a trial with success probability r until I see the first success. All the trials are independent of each other. What is the probability that you and I performed the same number of trials? Let Z be the total number of trials you and I performed altogether. Find the possible values and the probability mass function of Z.