You need to design a pair of dice where each number one 1-12 has an equal chance of being rolled. You have been given the task of designing the new dice. You are to use 2 standard cubes each with six faces, and number them in such a way that the probability of rolling the numbers (the sums of the two up faces) one through1-12 are the same.

What's the answer, and how would I find it.

Guest Feb 15, 2015

#1**+10 **

Try this:

Label one die with the numbers: 2, 4, 6, 8, 10, and 12.

Label the other die with the numbers: -1, -1, -1, 0, 0, and 0.

When the second die shows a -1, the sum of the two dice will be 1, 3, 5, 7, 9, or 11.

When the second die shows a 0, the sum of the two dice will be 2, 4, 6, 8, 10, or 12.

Since there is an equal chance for the first second die to show a -1 or a 0,

there will be equal chances for the two dice to sum to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12.

geno3141
Feb 16, 2015

#4**+5 **

Could also have one die with faces numbered 1 to 6 as normal, and the other die with half the faces numbered 6 and half numbered zero.

Or one die with faces numbered 7 to 12, and the other die with half numbered -6 and half zero.

Or one die with faces numbered 13 to 18 and the other with half numbered -12 and half numbered -6.

Or one die with ...!!!

.

Alan
Feb 16, 2015

#5**+5 **

So.....by Alan's reasoning ....the general solution would be for one die to have six faces labeled n, n+1, n+ 2, n+3, n + 4 and n+ 5 for n ≥ 1. And the other die would have three faces labeled -n + 1 and three labeled -n + 7

CPhill
Feb 16, 2015