If a pair of dice, one green and one red is rolled, what is the probability that the sum of the two dice is a number between five and ten, inclusive
To find the probability that the sum of the two dice is between five and ten (inclusive), we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
There are a total of $6 \times 6 = 36$ possible outcomes when rolling two dice, as each die has 6 sides.
The favorable outcomes are when the sum of the two dice is 5, 6, 7, 8, 9, or 10.
We can list the favorable outcomes:
Sum of 5: (1,4),(2,3),(3,2),(4,1) - 4 outcomes
Sum of 6: (1,5),(2,4),(3,3),(4,2),(5,1) - 5 outcomes
Sum of 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) - 6 outcomes
Sum of 8: (2,6),(3,5),(4,4),(5,3),(6,2) - 5 outcomes
Sum of 9: (3,6),(4,5),(5,4),(6,3) - 4 outcomes
Sum of 10: (4,6),(5,5),(6,4) - 3 outcomes
Total number of favorable outcomes = 4 + 5 + 6 + 5 + 4 + 3 = 27
Probability = number of favorable outcomes / total number of possible outcomes
= 27 / 36
= 3 / 4
Therefore, the probability that the sum of the two dice is a number between five and ten (inclusive) is $\frac{3}{4}$.
To find the probability that the sum of the two dice is between five and ten (inclusive), we need to determine the number of favorable outcomes and the total number of possible outcomes.
Let's look at the possible sums that fall between five and ten: 5, 6, 7, 8, 9, and 10.
To calculate the probabilities, we need to find the number of favorable outcomes (combinations that give us the desired sums) and divide it by the total number of possible outcomes.
Here is a step-by-step breakdown:
Step 1: Counting the favorable outcomes:
- To get a sum of 5, there is only one combination possible: (1, 4), or (4, 1).
- For a sum of 6, there are two combinations: (1, 5), (5, 1), (2, 4), or (4, 2).
- For a sum of 7, there are six combinations: (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), or (4, 3).
- For a sum of 8, there are five combinations: (2, 6), (6, 2), (3, 5), (5, 3), or (4, 4).
- For a sum of 9, there are four combinations: (3, 6), (6, 3), (4, 5), or (5, 4).
- For a sum of 10, there are three combinations: (4, 6), (6, 4), (5, 5).
Total number of favorable outcomes = 1 + 2 + 6 + 5 + 4 + 3 = 21
Step 2: Counting the total number of possible outcomes:
Each dice has six sides, so the total number of possible outcomes is 6 * 6 = 36.
Step 3: Calculating the probability:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 21 / 36
Simplifying the fraction, we get:
Probability = 7 / 12
Therefore, the probability of rolling a number between five and ten (inclusive) on the pair of dice is 7/12, or approximately 58.33%.