What is the theoretical probability of rolling a sum of 6 one roll of two standard number cubes?
There are 36 possible outcomes when rolling two standard number cubes. To find the number of outcomes that result in a sum of 6, we can make a table:
| Cube 1 | Cube 2 | Sum |
|--------|--------|-----|
| 1 | 5 | 6 |
| 2 | 4 | 6 |
| 3 | 3 | 6 |
| 4 | 2 | 6 |
| 5 | 1 | 6 |
There are 5 outcomes that result in a sum of 6. Therefore, the theoretical probability of rolling a sum of 6 on one roll of two standard number cubes is:
$$\frac{\text{Number of outcomes resulting in a sum of 6}}{\text{Total number of possible outcomes}}=\frac{5}{36}\approx0.139$$
So the theoretical probability of rolling a sum of 6 on one roll of two standard number cubes is approximately 0.139 or 13.9%.
are you sure
Yes, I'm sure. The probability of rolling a sum of 6 on one roll of two standard number cubes is 5/36, which is approximately 0.139 or 13.9%.
To find the theoretical probability of rolling a sum of 6 on two standard number cubes, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Enumerate the favorable outcomes
To get a sum of 6, the possible outcomes are:
- (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1)
So, there are 5 favorable outcomes.
Step 2: Enumerate all possible outcomes
Since each dice has 6 possible outcomes (numbers 1 to 6), the total number of possible outcomes is 6 x 6 = 36.
Step 3: Calculate the probability
The theoretical probability is given by the ratio of favorable outcomes to the total number of possible outcomes.
So, the probability of rolling a sum of 6 on two standard number cubes is:
5 (favorable outcomes) / 36 (possible outcomes)
Therefore, the theoretical probability of rolling a sum of 6 on one roll of two standard number cubes is 5/36.