What is the expected value of sum of the numbers that appears when a pair of fair dice is rolled. 10 points?

Question

10 points for correct answer. The answer is 7 but i need to know how to get the answer.

Answer 1

E(X) = sum of n*P(n) from n=2 to n=12
E(X) = 2(1/36) + 3(2/36) + 4(3/36) + 5(4/36) + 6(5/36) + 7(6/36) + 8(5/36) + 9(4/36) + 10(3/36) + 11(2/36) + 12(1/36)
E(X) = 7

Answer 2

Because in the throwing of 2 fair dice, the highest probability is to get a 3 and a 4, a 2 and a 5, or a 1 and a 6.

Answer 3

There are 36 possible combinations, and the values will range from 2 to 12. Just make a chart of every possible combination, and see what the sum of each combination is. You will find that 7 is the most common sum.

Answer 4

there can be the following possibilities known as the sample space
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)
so chances of getting a sum of 2 will be 1/36
getting 3 will be 2/36 or =>1/18
getting a 4 will be 3/36=>1/12
getting a 5 will be 4/36=>1/9
getting a 6 will be 5/36
getting a 7 will be 6/36=>1/6
getting an 8 will be 5/36
getting a 9 will be 4/36=>1/9
gettin a 10 will be 3/36=>1/12
getting an 11 will be 2/36=>1/18
and getting a 12 will be 1/36
total of all these probabilities will be 1/36+2/36+3/36............=1
now draw whatever conclusions you want as the question and your suggested answers are a little ambiguous.if you mean
getting a sum of 7 has the greatest probability it is so .it is 1/6