Three contestants, \(A, B,\) and \(C,\) each has 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.