Platonic Sample Space

The construct of a "Platonic sample space" is a hypothetical pedagogical construct -- it is not a mathematical idea but, instead, a bridging form potentially enabling some cogntive entry into the conceptual domain. Drawing a sample from a random generator could be imagined as randomly selecting an event from its sample space. So, flipping a fair coin could be construed as choosing one of the two items in the [Heads; Tails] space (a space containing two individual coins, one showing Heads, and one showing Tails). Flipping two coins would be likened to drawing one pair out of a "Platonic hat" containing four possible compound events, each a unique pair [(Heads, Heads) (Heads, Tails) (Tails; Heads) (Tails, Tails)]. Yet this Platonic space is homologous with the random generator's sample space only for the special case where all events are equally likely. Flipping a loaded coin with a .75 chance of landing on Heads would be analogous to choosing from a “corrected” space, “Heads; Heads; Heads; Tails.” [read more]