In the board game of "Aggravation", the game begins with each player having their four game pieces in a "base" holding area and a player is unable to place one of her game pieces on the board for play until they role either a one or a six with a fair die.

(a) Define a probability model that can be used to assign probability to events involving the number of times that a player must roll the fair die to obtain a one or a six.

(b) What is the probability that it will take three or more rolls of the die for a player to get their first game piece on the board?

(c) What is the expected number of rolls of the die for a player to get their first game piece on the board?

(d) Define a new probability model, if you need to, and derive the expected number of rolls of the die for a player to get all four of their initial game pieces on the board.