Let the experiment be the toss of three dice in a row.

Let X be the outcome of the 1st die.

Let Y be the outcome of the 2nd die.

Let Z be the outcome of the 3rd die.

Let A be the event that X > Y ,

let B be the event that Y > Z,

let C be the event that X > Z.

a) Find P(A).

b) Find P(B).

c) Find P(A ? B).

d) Are A and B independent?

e) Are A,B,C pairwise independent?

f) Find (A ? B ? C)?

g) Are A,B,C mutually independent?