two regular 6 sided dice are tossed compute the probability of rolling an 8
To calculate the probability of rolling an 8 with two regular 6-sided dice, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
The possible outcomes when rolling two dice can be represented on a table or a matrix, where each cell represents the outcome of one die.
The sum of the numbers on the two dice ranges from 2 to 12. To calculate the probability of rolling an 8, we need to count the number of cells that have an 8.
| Dice 1 | Dice 2 | Sum |
|--------|--------|-----|
| 1 | 1 | 2 |
| 1 | 2 | 3 |
| 1 | 3 | 4 |
| 1 | 4 | 5 |
| 1 | 5 | 6 |
| 1 | 6 | 7 |
| 2 | 1 | 3 |
| 2 | 2 | 4 |
| 2 | 3 | 5 |
| 2 | 4 | 6 |
| 2 | 5 | 7 |
| 2 | 6 | 8 |
| 3 | 1 | 4 |
| 3 | 2 | 5 |
| 3 | 3 | 6 |
| 3 | 4 | 7 |
| 3 | 5 | 8 |
| 3 | 6 | 9 |
| 4 | 1 | 5 |
| 4 | 2 | 6 |
| 4 | 3 | 7 |
| 4 | 4 | 8 |
| 4 | 5 | 9 |
| 4 | 6 | 10 |
| 5 | 1 | 6 |
| 5 | 2 | 7 |
| 5 | 3 | 8 |
| 5 | 4 | 9 |
| 5 | 5 | 10 |
| 5 | 6 | 11 |
| 6 | 1 | 7 |
| 6 | 2 | 8 |
| 6 | 3 | 9 |
| 6 | 4 | 10 |
| 6 | 5 | 11 |
| 6 | 6 | 12 |
From the table, we can see that there are 5 cells that have an 8 as the sum of the two dice.
Therefore, the number of favorable outcomes is 5, and the total number of possible outcomes is 36 (since each die has 6 sides, resulting in 6 x 6 = 36 possible outcomes).
To calculate the probability of rolling an 8, we divide the number of favorable outcomes (5) by the total number of possible outcomes (36):
P(rolling an 8) = favorable outcomes / total outcomes
P(rolling an 8) = 5/36
Therefore, the probability of rolling an 8 with two regular 6-sided dice is 5/36.
To calculate the probability of rolling an 8 with two regular 6-sided dice, we can determine the number of favorable outcomes (rolling an 8) divided by the total number of possible outcomes.
Let's list down the possible combinations of rolls that can add up to 8:
1 + 7 (not possible as one die only has 6 sides)
2 + 6
3 + 5
4 + 4 (two possibilities, as both dice can show a 4)
5 + 3
6 + 2
Counting these combinations, there are 5 favorable outcomes.
Now, let's consider the total number of possible outcomes. Since we have two dice, each with 6 sides, the total number of outcomes is 6 * 6 = 36.
Therefore, the probability of rolling an 8 is given by: favorable outcomes / total outcomes = 5 / 36.
Hence, the probability of rolling an 8 with two regular 6-sided dice is 5/36 or approximately 0.139 (rounded to three decimal places).