Question

For the following exercises, two dice are rolled, and the results are summed. 

Construct a table showing the sample space of outcomes and sums.

Answer 1

Consider rolling of two dice and summed the results.

When a die is rolled, there are six possible outcomes: {1, 2, 3, 4, 5, 6}

 

Using the multiplication principle, number of total possible outcomes when two dice are rolled is,

6 × 6 = 36

 

For each outcome in first coin, there are six possible outcomes in second dice. All possible outcomes in the rolling of two dice are,

{(1, 1), (1, 2), …,(1, 6), (2, 1), (2, 2), … ,(2, 6), (3, 1), (3, 2), … ,(3, 6), (4, 1), (4, ), … ,(4, 6)  (5, 1), (5, 2), … ,(5, 6), (6, 1), (6, 2), … , (6, 6)}

 

As the results are added to get the outcome, the possible outcomes of the given experiment will be any number from 2 to 12.

 

Following table shows all the possible outputs in the rolling of two dice,

Sum	Outcomes
2	(1, 1)
3	(1, 2), (2, 1)
4	(1, 3), (2, 2), (3, 1)
5	(1, 4), (2, 3), (3, 2), (4, 1)
6	(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
7	(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
8	(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
9	(3, 6), (4, 5), (5, 4), (6, 3)
10	(4, 6), (5, 5), (6, 4)
11	(5, 6), (6, 5)
12	(6, 6)

 

Therefore, sample space for the given experiment is,

S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Sample space for the given experiment is,

S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}