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 $\frac{3}{4}$.
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
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