On Thu, 29 Jun 2000, GEORGE PERKINS wrote:
> Recently a colleague came in the office with the following problem:
>
> Is there a way to 'load' two individual die so that all sums will be
> equally likely?
> (I take it that they would like to load the die in such a way that the
> sum of 2 is equally likely as a sum of 3, as a sum of 4...etc)
If we are referring to standard cubical dice with 1, 2, ..., 6 pips on
each face, the answer is "No." If the faces are renumbered, something
like that would be possible, even without "loading" the dice.
For a simple (some might say 'degenerate') example, consider a die
with one pip on each face, and a second die with two pips on each face.
The sum is invariably 3. For a more interesting example, with more than
one possible sum, let one die have one pip on three faces, and two pips
on the other three; and let the other die have two pips on three faces
and four pips on the other three. The possible sums are 3, 4, 5, and 6,
each of which can be obtained in any of 9 ways, and are therefore
equally probable if the dice are "fair". No need to load them.
More complex examples are clearly possible, and are left as
exercises for the reader.
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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