Aha! a better graphic!

In my probability class, I’ve been teaching my students about joint
probability mass functions with two random variables that are not independent.  Since this is a new concept, I use a very simple example.

Let X be random variable determined
by the roll of a single fair die, so X = 1, 2, …, 6, each with
probability 1/6.  Let Y be a random integer in the range 1, …,
X, each value having equal probabilities 1/X.  (In other words, we
have the marginal pmf f(x) = 1/6, and the conditional pmf f(y|X) =
1/X.)  Find the marginal pmf f(y), for Y.

Until today, I was very confused about how to represent this
graphically; I drew an assortment of confusing pictures to show what
was going on.  Then I read this
at J. D. Fisher’s thought-provoking MathandText blog. 
Voila!  The correct graphic practically drew itself (except for an
hour of Mathematica hacking).