1.11. Three contestants, A, B, and C, each have a balloon and a pistol. From fixed positions, they fire at each other’s balloons. When a balloon is hit, its owner is out. When only one balloon remains, its owner gets a $1000 prize. At the outset, the players decide by lot the order in which they will fire, and each player can choose any remaining balloon as his target. Everyone knows that A is the best shot and always hits the target, that B hits the target with probability .9, and that C hits the target with probability .8. Which contestant has the highest probability of winning the $1000?

Explain why.