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?