Hi, I'm struggling to understand probability coupling. I have the following problem:

Let X and Y each be uniformly distributed on the discrete set {1,...6} (i.e. the distribution of the roll of 1 fair die).

(a) If X and Y are independent, what is Pr[X = Y]?

(b) Couple X and Y so that Pr[X = Y] = 1.

(c) Couple X and Y so that Pr[X > Y] = 5/6.

I'm not entirely sure where to start and can't find much information on it.

For part (b), would I be right in simply saying "Let X={1,2,...,6} and let Y={X}. Thus, Pr[X = Y] = 1." If so, great but if not where am I going wrong?

Thanks for your help.