Homework SourseA pair of dice is rolled and the larger of the two numbers i
A pair of dice is rolled, and the larger of the two numbers is recorded. Find the probability distribution for this experiment. A pair of dice is rolled and the smaller of the two numbers is recorded. Find the probability distribution for this experiment.
Solution
Consider the following sample space, the larger and smaller outcomes are observed as:
So, Probability distribution of larger outcome (X):
Probability distribution of smaller outcome (Y):
| 1st Dice | 2nd Dice | Larger outcome | Smaller outcome |
| 1 | 1 | 1 | 1 |
| 1 | 2 | 2 | 1 |
| 1 | 3 | 3 | 1 |
| 1 | 4 | 4 | 1 |
| 1 | 5 | 5 | 1 |
| 1 | 6 | 6 | 1 |
| 2 | 1 | 2 | 1 |
| 2 | 2 | 2 | 2 |
| 2 | 3 | 3 | 2 |
| 2 | 4 | 4 | 2 |
| 2 | 5 | 5 | 2 |
| 2 | 6 | 6 | 2 |
| 3 | 1 | 3 | 1 |
| 3 | 2 | 3 | 2 |
| 3 | 3 | 3 | 3 |
| 3 | 4 | 4 | 3 |
| 3 | 5 | 5 | 3 |
| 3 | 6 | 6 | 3 |
| 4 | 1 | 4 | 1 |
| 4 | 2 | 4 | 2 |
| 4 | 3 | 4 | 3 |
| 4 | 4 | 4 | 4 |
| 4 | 5 | 5 | 4 |
| 4 | 6 | 6 | 4 |
| 5 | 1 | 5 | 1 |
| 5 | 2 | 5 | 2 |
| 5 | 3 | 5 | 3 |
| 5 | 4 | 5 | 4 |
| 5 | 5 | 5 | 5 |
| 5 | 6 | 6 | 5 |
| 6 | 1 | 6 | 1 |
| 6 | 2 | 6 | 2 |
| 6 | 3 | 6 | 3 |
| 6 | 4 | 6 | 4 |
| 6 | 5 | 6 | 5 |
| 6 | 6 | 6 | 6 |
