need a pair of dice where each number from 1 - 12 has an equal chance of being rolled. You have been given the task of designing the new dice for the board game. You are to use two standard cubes (each with six faces) and number them in such a way that the probability of rolling the numbers 1 - 12 are the same.
the answer must include a table indication how each number 1 - 12 can be achieved the same number of times.
How can you roll a 1 with 2 dice ??
One of the dice has to have a 0...you are making a new set of dice for a new game
no
To design a pair of dice where each number from 1 to 12 has an equal chance of being rolled, we can use two standard cubes and assign numbers to their faces in a specific way.
Here's a method for numbering the faces that satisfies the given condition:
Cube 1:
- Face 1: Assign number 1
- Faces 2 to 5: Leave them blank or unnumbered
- Face 6: Assign number 2
Cube 2:
- Faces 1 and 6: Assign number 3
- Face 2: Assign number 4
- Face 3: Assign number 5
- Face 4: Assign number 6
- Faces 5 and 6: Leave them blank or unnumbered
By using these numbers for the faces of each cube, we can generate each number from 1 to 12 with an equal probability.
Here's a table that shows how each number from 1 to 12 can be achieved an equal number of times:
Number | Cube 1 | Cube 2
-------|--------|-------
1 | 1 |
2 | 6 | 2, 3
3 | | 1, 3, 4
4 | | 1, 4, 5
5 | | 1, 5, 6
6 | | 1, 6
7 | | 3, 4
8 | | 3, 5
9 | | 3, 6
10 | | 4, 5
11 | | 4, 6
12 | | 5, 6
In this table, the numbers in each cell indicate which faces of Cube 1 and Cube 2 need to be rolled to achieve the corresponding number. For example, to roll a 2, you would roll Face 1 of Cube 1 and Face 2 of Cube 2.
By following this numbering scheme and rolling the two cubes together, you will ensure that each number from 1 to 12 has an equal chance of being rolled.