(a) Using two states of the world describe the following situation, specifying how each state differs from the other: "Roger ascribes probability 0.4 to the Philadelphia Phillies winning the World Series."

(b) Add to the two states of the world that you listed above two more states of the world, and use the four states to construct a belief space in which the following situation is represented as a state of the world: "Jimmy ascribes probability 0.3 to the Philadelphia Phillies winning the World Series and to Roger ascribing probability 0.4 to the Philadelphia Phillies winning the World Series, and Jimmy ascribes probability 0.7 to the Philadelphia Phillies not winning the World Series and to Jimmy ascribing 0.4 to the Philadelphia Phillies winning the World Series."

(c) Construct a belief space in which the following situation is represented by a state of the world and indicate that state. Roger says:

* I ascribe probability 0.3 to "the Philadelphia Phillies will win the World Series, and Jimmy ascribes probability 0.3 to the Philadelphia Phillies winning the World Series and to my ascribing 0.4 to the Philadelphia Phillies winning the World Series, and Jimmy ascribes probability 0.7 to the Philadelphia Phillies not winning the World Series and to my ascribing 0.4 to the Philadelphia Phillies winning the World Series."

* I ascribe probability 0.2 to "the Philadelphia Phillies will win the World Series, and Jimmy ascribes probability 0.7 to the Philadelphia Phillies winning the World Series and to my ascribing 0.5 to the Philadelphia Phillies winning the World Series, and Jimmy ascribes probability 0.3 to the Philadelphia Phillies not winning the World Series and to my ascribing 0.5 to the Philadelphia Phillies winning the World Series."

* I ascribe probability 0.4 to "the Philadelphia Phillies will win the World Series, and Jimmy ascribes probability 0.2 to the Philadelphia Phillies winning the World Series and to my ascribing 0.1 to the Philadelphia Phillies winning the World Series, and Jimmy ascribes probability 0.8 to the Philadelphia Phillies not winning the World Series and to my ascribing 0.1 to the Philadelphia Phillies winning the World Series."

* I ascribe probability 0.1 to "the Philadelphia Phillies will win the World Series, and Jimmy ascribes probability 0.6 to the Philadelphia Phillies winning the World Series and to my ascribing 0.4 to the Philadelphia Phillies winning the World Series, and Jimmy ascribes probability 0.4 to the Philadelphia Phillies not winning the World Series and to my ascribing 0.3 to the Philadelphia Phillies winning the World Series."