1. Sample space:
{2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12}
2. Probabilities of getting each sum
Probability of getting 2: 1/36Probability of getting 3: 1/18Probability of getting 4: 1/12Probability of getting 5: 1/9Probability of getting 6: 5/36Probability of getting 7: 1/6Probability of getting 8: 5/36Probability of getting 9: 1/9Probability of getting 10: 1/12Probability of getting 11: 1/18Probability of getting 12: 1/36
Explanation:
1. Sample space.
Sample space is the set consituted by the total possible outcomes. Since each number cube has 6 possible outcomes, the number of possible outcomes when you toss two number cubes is 6×6 = 36. Thus, your sample space must have 36 elements.
You can found the sample space using a chart:
123456
1234567
2345678
3456789
45678910
567891011
6789101112
Hence, the sample space is the set of all the numbers inside the square:
{2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12}
2. Probabilities of getting each sum.
The probability of getting each sum is the number of times each sum appear in the sample space divided by the size of the sample space (36):
Probability of getting 2:
1/36
Probability of getting 3:
2/36 = 1/18
Probability of getting 4:
3/36 = 1/12
Probability of getting 5:
4/36 = 1/9
Probability of getting 6:
5/36
Probability of getting 7:
6/36 = 1/6
Probability of getting 8:
5/36
Probability of getting 9:
4/36 = 1/9
Probability of getting 10:
3/36 = 1/12
Probability of getting 11:
2/36 = 1/18
Probability of getting 12:
1/36
