Question

An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.

Answer 1

The numbers on the die are 1,2,3,4,5,6.

The outcomes when a die is rolled is twice can be:

X= {(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)}

The sum can be calculated as:

X= {(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)}

Therefore, outcome can be summarised as:

n(X) be the number of times that number comes.

X	2	3	4	5	6	7	8	9	10	11	12
n(X)	1	2	3	4	5	6	5	4	3	2	1