three fair dice are tossed. Let X,Y,Z denote the respetive numbers showing on their top faces. Assume X,Y,Z are independent.

Question

a) find P(X<Y)
b) Show that the events (X<Y) and (Y<Z) are NOT independent

heeelp...

Answer 1

P(X<Y) + P(X=Y) + P(X>Y) = 1

P(X>Y) = P(X<Y) by symmetry and
P(X=Y)=1/6, therefore:

P(X<Y) = 5/12