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 5 and 10 inclusive
To find the probability, we first need to determine the total number of outcomes when rolling a green and a red die. Since each die has 6 sides, the total number of outcomes is 6 * 6 = 36.
Next, we need to determine the number of outcomes where the sum of the two dice is a number between 5 and 10 inclusive. We can do this by listing out all possible outcomes:
- (1, 4) - (4, 1)
- (1, 5) - (5, 1)
- (1, 6) - (6, 1)
- (2, 3) - (3, 2)
- (2, 4) - (4, 2)
- (2, 5) - (5, 2)
- (2, 6) - (6, 2)
- (3, 4) - (4, 3)
- (3, 5) - (5, 3)
- (3, 6) - (6, 3)
- (4, 5) - (5, 4)
- (4, 6) - (6, 4)
- (5, 6) - (6, 5)
- (6, 6)
There are 14 possible outcomes where the sum is between 5 and 10.
Therefore, the probability is 14/36 = 7/18.
To calculate the probability of obtaining a sum between 5 and 10 (inclusive) when rolling a pair of dice, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
1. Total number of possible outcomes:
When rolling a pair of dice, each dice has 6 possible outcomes (numbers 1 to 6). Therefore, the total number of possible outcomes is 6 x 6 = 36.
2. Total number of favorable outcomes (sum between 5 and 10):
There are multiple combinations of numbers on the two dice that result in a sum between 5 and 10. We can summarize these combinations:
- Sum 5: (1, 4), (2, 3), (3, 2), (4, 1) - total of 4 combinations
- Sum 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) - total of 5 combinations
- Sum 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) - total of 6 combinations
- Sum 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) - total of 5 combinations
- Sum 9: (3, 6), (4, 5), (5, 4), (6, 3) - total of 4 combinations
- Sum 10: (4, 6), (5, 5), (6, 4) - total of 3 combinations
The total number of favorable outcomes is 4 + 5 + 6 + 5 + 4 + 3 = 27.
3. Probability calculation:
To find the probability, divide the total number of favorable outcomes by the total number of possible outcomes:
Probability = Total number of favorable outcomes / Total number of possible outcomes
= 27 / 36
= 3 / 4
= 0.75
Therefore, the probability of obtaining a sum between 5 and 10 (inclusive) when rolling a pair of dice is 0.75 or 75%.