if two dice are rolled what is the probability that the sum of the dots on the upwards faces is 8?
possible outcomes
1 | 1 2 3 4 5 6
2 | 1 2 3 4 5 6
3 | 1 2 3 4 5 6
4 | 1 2 3 4 5 6
5 | 1 2 3 4 5 6
6 | 1 2 3 4 5 6
of those 36, 5 of them add to 8
To find the probability of obtaining a sum of 8 when two dice are rolled, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Total number of possible outcomes when two dice are rolled: Each die has 6 faces, so the total number of outcomes is 6 * 6 = 36.
Now let's calculate the number of favorable outcomes (the outcomes where the sum is 8):
Possible combinations of numbers on the dice when the sum is 8:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)
So, there are 5 favorable outcomes.
Therefore, the probability of obtaining a sum of 8 when two dice are rolled is 5/36.
To find the probability of rolling a sum of 8 with two dice, you need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Determine the favorable outcomes
The favorable outcomes are the different combinations of dice rolls that result in a sum of 8.
To find the pairs of numbers that sum to 8, you can create a table listing all possible outcomes of rolling two dice:
| Dice 1 | Dice 2 | Sum |
|--------|--------|-----|
| 1 | 7 | - |
| 2 | 6 | - |
| 3 | 5 | 8 |
| 4 | 4 | 8 |
| 5 | 3 | 8 |
| 6 | 2 | - |
| 7 | 1 | - |
From the table, we can see that there are three favorable outcomes: (3, 5), (4, 4), and (5, 3).
Step 2: Determine the total number of possible outcomes
To find the total number of possible outcomes, consider that each dice has 6 possible outcomes (the numbers 1-6). Since there are two dice being rolled, there are 6 * 6 = 36 possible outcomes.
Step 3: Calculate the probability
Finally, divide the number of favorable outcomes (3) by the total number of possible outcomes (36) to find the probability:
P(sum of 8) = Favorable outcomes / Total outcomes
= 3 / 36
= 1 / 12
Therefore, the probability that the sum of the dots on the upward faces of two dice is 8 is 1/12, or approximately 0.0833.