# Rolling with the Same Probability

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to complete this sentence:
Rolling a sum of ___ on two ___-sided dice is the same probability as rolling a sum of ___ on two ___-sided dice.

### Hint

How could we organize the possible values to see this visually?
How many possible answers are there?

Thank you to the secondary mathematics teachers from San Marcos Unified School District for these great answers:
Rolling a 9 on two 6-sided dice is the same probability as rolling a 2 on two 3-sided dice.
Rolling a 2 on two 4-sided dice is the same probability as rolling a 5 on two 8-sided dice.
Rolling a 3 (or 7) on two 4-sided dice is the same probability as rolling a 9 on two 8-sided dice.
Finally Robert Gordon found that you get a 0% probability from rolling a 9 on two 1-sided dice which is the same probability as rolling an 8 on two 3-sided dice.

Source: Audrey Mendivil, Daniel Luevanos, and Robert Kaplinsky

## Similar Triangles And Slope

Directions: The three triangles on the line are similar. Using the digits 0 to 9 …

1. Is it possible to construct a 3 sided die?

2. You can also roll a sum of 2 on 3-sided dice and a sum of 5 on 6-sided dice, both of which have a probability of 1/9.

3. Rolling a nine on two six sided dice is the same as rolling a 2 on two 3 sided dice.

4. Rolling a 2 on two 4-sided dice is the same as rolling a 5 on two 8-sided dice

5. Rolling a 9 on two 6-sided dice is the same probability as rolling a 2 on two 3-sided dice.

6. timtimertinmctim

rolling a 2 and a 4 and a 5 and a 8 is the same.

7. Rolling a 9 on two 6-sided dice is the same probability as rolling a 2 on two 3-sided dice.