Consider an experiment in which a coin that comes up heads with proba- bility p is tossed until heads is obtained for the rst time. If this experiment is performed twice (and the outcomes are independent), what is the proba- bility that the same number of tails prior to the rst heads will be realized in both experiments? Hint: Let X1 be the number of tails prior to the rst heads when the rst coin is tossed; let X2 be the number of tails prior to the rst heads when the second coin is tossed. What is P [X1 = x; X2 = x]? 2