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Answer:
Step-by-step explanation:
Each die has faces numbered from 1 to 6. Hence, the sums range from 2 to 12.
There are 6 × 6 = 36 possible combinations of the dice.
The sums, their possible combinations and their probabiities are as below:
2 = 1+1 1/36
3 = 1+2 = 2+1 2/36= 1/18
4 = 1+3 = 2+2 = 3+1 3/36= 1/12
5 = 1+4 = 2+3 = 3+2 = 4+1 4/36= 1/9
6 = 1+5 = 2+4 = 3+3 = 4+2 = 5+1 5/36
7 = 1+6 = 2+5 = 3+4 = 4+3 = 5+2 = 6+1 6/36= 1/6
8 = 2+6 = 3+5 = 4+4 = 5+3 = 6+2 5/36
9 = 3+6 = 4+5 = 5+4 = 6+3 4/36= 1/9
10 = 4+6 = 5+5 = 6+4 3/96= 1/12
11 = 5+6 = 6+5 2/36= 1/18
12 = 6+6 1/36
Sum of probabilities = 1/36 + 1/18 + 1/12 + 1/9 + 5/36 + 1/6 + 5/36 + 1/9 + 1/12 + 1/18 + 1/36 = 1
1)
2) The average value of X = 1/36*(2+12) + 1/18*(3+11) + 1/12*(4+10)+ 1/9(5+9)+ 5/36(6+8)+ 1/6(7) = 14*(5/6)+7/6 = 77/6