Homework SourseDetermine the probability that the product of the two rolls
Determine the probability that the product of the two rolls (two dice) is greater than the sume of the two rolls.
Solution
Consider the table:
As we see, there are 36 cases, in 24 such cases the product is greater than the sum.
Thus,
P(product is greater than sum) = 24/36 = 2/3 = 0.66666666667 [answer]
| Die 1 | Die 2 | Sum | Product |
| 1 | 1 | 2 | 1 |
| 1 | 2 | 3 | 2 |
| 1 | 3 | 4 | 3 |
| 1 | 4 | 5 | 4 |
| 1 | 5 | 6 | 5 |
| 1 | 6 | 7 | 6 |
| 2 | 1 | 3 | 2 |
| 2 | 2 | 4 | 4 |
| 2 | 3 | 5 | 6 |
| 2 | 4 | 6 | 8 |
| 2 | 5 | 7 | 10 |
| 2 | 6 | 8 | 12 |
| 3 | 1 | 4 | 3 |
| 3 | 2 | 5 | 6 |
| 3 | 3 | 6 | 9 |
| 3 | 4 | 7 | 12 |
| 3 | 5 | 8 | 15 |
| 3 | 6 | 9 | 18 |
| 4 | 1 | 5 | 4 |
| 4 | 2 | 6 | 8 |
| 4 | 3 | 7 | 12 |
| 4 | 4 | 8 | 16 |
| 4 | 5 | 9 | 20 |
| 4 | 6 | 10 | 24 |
| 5 | 1 | 6 | 5 |
| 5 | 2 | 7 | 10 |
| 5 | 3 | 8 | 15 |
| 5 | 4 | 9 | 20 |
| 5 | 5 | 10 | 25 |
| 5 | 6 | 11 | 30 |
| 6 | 1 | 7 | 6 |
| 6 | 2 | 8 | 12 |
| 6 | 3 | 9 | 18 |
| 6 | 4 | 10 | 24 |
| 6 | 5 | 11 | 30 |
| 6 | 6 | 12 | 36 |
