Peter and mary take turns throwing one dart at the dartboard. peter hits the bullseye with probability p and mary hits the bullseye with prob- ability r. whoever hits the bullseye first wins. suppose peter throws the first dart. (a) what is the probability that mary wins? b) let x be the number of times mary throws a dart in the game. find the possible values and the probability mass function of x. check that the function you give sums to 1. is this a familiar named distribution? c) find the conditional probability p(x = kl mary wins), for all possible values k of x. is this a familiar named distribution?