Worked solution
Sum two tetrahedral dice
Two fair tetrahedral dice, each with faces 1, 2, 3 and 4, are thrown. The score is the sum of their two numbers. Let denote the score. Find the probability distribution of .
CJC · Lecture · Example 1
List every ordered score pair
Let and be the scores on the first and second die. Under the source model of independent fair dice, all sixteen ordered pairs have probability . The source sum table has as rows and as columns:
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 |
| 2 | 3 | 4 | 5 | 6 |
| 3 | 4 | 5 | 6 | 7 |
| 4 | 5 | 6 | 7 | 8 |
How did this part go?
Group equal sums and check the total
The sums occur in cells respectively.
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
|---|---|---|---|---|---|---|---|
Check the probabilities, as emphasized in the Teacher note: . Every probability lies between zero and one.
How did this part go?
Common mistakes
The seven sums are not equally likely. Count the sixteen equally likely ordered die outcomes first; fairness of each die alone does not establish independence.