Question 330445
a) Look at all of the possible rolls and their sum.
1	2	3
1	3	4
1	4	5
1	5	6
1	6	7
1	6	7
1	2	3
1	3	4
1	4	5
1	5	6
1	6	7
1	6	7
2	2	4
2	3	5
2	4	6
2	5	7
2	6	8
2	6	8
3	2	5
3	3	6
3	4	7
3	5	8
3	6	9
3	6	9
4	2	6
4	3	7
4	4	8
4	5	9
4	6	10
4	6	10
5	2	7
5	3	8
5	4	9
5	5	10
5	6	11
5	6	11
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There are 36 possible outcomes,
Sum of 3:2, {{{P(3)=2/36=1/18}}}
Sum of 4:3, {{{P(4)=3/36=1/12}}}
Sum of 5:4, {{{P(5)=4/36=1/9}}}
Sum of 6:5, {{{P(6)=5/36}}}
Sum of 7:8, {{{P(7)=8/36=2/9}}}
Sum of 8:5, {{{P(8)=5/36}}}
Sum of 9:4, {{{P(9)=4/36=1/9}}}
Sum of 10:3, {{{P(10)=3/36=1/12}}}
Sum of 11:2, {{{P(11)=2/36=1/18}}}
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Sum the product of the sum and the probability,
{{{A=3(1/18)+4(1/12)+5(1/9)+6(5/36)+7(2/9)+8(5/36)+9(1/9)+10(1/12)+11(1/18)}}}
{{{A=7}}}
As expected since the probabilities are symmetric about {{{7}}}.