you have all heard of a duel... but what about a truel... well... a truel is a duel with three people... in this specific truel, there are three gentlemen players who each wait their turn before they shoot. player 1 will hit the person he shoots at with probability x player 2 will hit the person he shoots at with probability y player 3 will hit the person he shoots at with probability z x>y>z a couple of other things about the game... each person knows how good of a shot the other is. (i.e. player 1,2,3 know x,y,z). also, there is no chance that player 2 will die if player 1 shoots at 3. that is, if player 1 misses his intended target, noone else will be hit. and finally, each player must try to hit someone each turn. what is the probability that player 1 wins? player 2? player 3?