In the game of RISK, two players compete in a game of dice rolling for conquest of the world. One player is on “offense” while the other is on “defense.” For this problem, the player on offense is allowed to roll multiple dice while the player on defense rolls a single die. Whoever rolls the higher number wins (i. e., the highest number rolled by the offense is compared with the number rolled by the defense). In case of a tie, the defense is declared the winner. The loser must remove one army from the board. Find the probability of the offense winning and the probability of the defense winning in each of the following scenarios:
(a) Both players roll only a single die.
(b) Offense rolls two dice while defense rolls one die.
(c) Offense rolls three dice while defense rolls one die.