A fair, six-sided dice is rolled two times. Let X1 and X2 denote the number of points showing on the first and second rolls, respectively. Let U=X1-X2, and V=X1+X2.

Show that U and V are not independent.

I want to show that the probability of the intersection of two events, is not equal to the product of two individual probabilities.

So, I am using this formula: P(U and V)= P(U)*P(V). I want to show that the left hand side of the formula does not hold.

How do I go from there? I changed the U and V with the values but I am stuck from here. Can anyone please explain or direct me?

Thanks,