Question

Find the sample space associated with the experiment of rolling a pair of dice (plural of die). Also find the number of elements of the sample space.

Answer 1

Hint: First of all, we should know the definition of sample space. The sample space is defined as the set of all possible outcomes (or) results of an experiment. So, we have to find all the possible outcomes obtained from rolling the dice. We have to mention all the possible outcomes. Now, we have to count all the possible outcomes. This represents the total number of elements of the sample space.

Complete step-by-step solution -
Before solving the question, we should understand the definition of sample space. The sample space is defined as the set of all possible outcomes (or) results of an experiment.
From the question, it is clear that we have to find the sample space of rolling a pair of dice.
Let us assume two pairs die. First die is represented as die A and the second die is represented as die B.
Let us draw a table. In this table, the first column represents a certain outcome on die A. The second column represents the possible outcomes on die B. The third column represents the total number of outcomes occurred.

S. No	Number on Die A	Possible outcome on Die B	Number of outcomes
1	1	1,2,3,4,5,6	6
2	2	1,2,3,4,5,6	6
3	3	1,2,3,4,5,6	6
4	4	1,2,3,4,5,6	6
5	5	1,2,3,4,5,6	6
6	6	1,2,3,4,5,6	6

From the above table, we get all the elements of sample space.
The elements in the sample space are:
(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).
From the table, we get the total number of outcomes \[=6+6+6+6+6+6=36\].
Hence, the total number of elements in sample space =36.

Note: It is better to write all the outcomes in the form of a table. After mentioning in the table, we have to write all the possible outcomes. This will give a clear view for counting the total number of outcomes and we will not miss any outcome. If we write them directly there may be a chance of missing an outcome (or) they may be a chance of counting mistakes. So, students should be careful while solving this question.