Die A had two 5s, three 3s, and one 1 on its six faces; die B has two 2s and four 4s on its six faces. Both dice are fair. Each player simultaneously rolls one of the dice, and the winner is the player with the higher number showing.
a) If you want to win, would you rather roll die A or B?
b) If the winner receives the dollar amount of whatever number shows on that player's winning die, what are the expected winnings for each player?