Urn
Urn
[Cueball is standing in a classroom with Megan at a desk.] Cueball: Imagine that you're drawing at random from an urn containing fifteen balls - six red and nine black. Megan: OK. I reach in and... ...My grandfather's ashes?!? Oh God! Cueball: I... what? Megan: Why would you do this to me?!?

A common tool for explaining concepts in elementary probability theory are games involving the drawing of coloured balls from a container, such as a bag, or hat. In older statistics related texts, a convention developed of describing the container as an urn. This is so common that such problems are often called urn problems .
While an urn can have many uses, in modern times the most common context in which it is used is to contain the burned remains of deceased individuals after a cremation . This is likely because as interior decor has grown more minimalist, other types of urn became less common and the association of the word urn with cremation has become ubiquitous in the vernacular.
Megan , when asked to imagine drawing balls from an urn, imagines a cremation urn containing not only balls, but also human remains. She may be referring to a real grandfather who has been cremated, or is simply improvising a joke at Cueball's expense.
The title text refers to two distinct scenarios in the coloured ball experiment: The balls may be replaced between each drawing, or not. In the former case, each draw is independent of the previous, in the latter the chances of picking a particular (remaining) ball the next time have increased. Megan (or rather Randall if it is he who speaks in the title text) would prefer to put the ashes back into the urn. She might also want to have her grandfather back, and be playing with the word "replacement".
The distinction between repeated drawing with and without replacement is used in most presentations of elementary probability because it illustrates a subtle but important theoretical distinction: if the balls are replaced, one at a time, before drawing the next, the number of balls of a certain colour has the binomial distribution , but if the balls are not replaced, so that the same ball cannot be drawn twice, you instead get the hypergeometric distribution .
There are myriad reasons why Megan would want to draw with replacement, the most simple of which being that she has nowhere to put ashes other than in their designated urn. Ashes by their nature need a container, or they will make a mess; cremated remains in particular come with the additional requirement that the container be respectful to the deceased.
[Cueball is standing in a classroom with Megan at a desk.] Cueball: Imagine that you're drawing at random from an urn containing fifteen balls - six red and nine black. Megan: OK. I reach in and... ...My grandfather's ashes?!? Oh God! Cueball: I... what? Megan: Why would you do this to me?!?
