Question

Two dice are thrown. Describe the sample space of this experiment.

Answer 1

Hint:
1) If two dice are thrown, there are 6 × 6 = 36 different outcomes possible.
2) The sample space of a random experiment is the set of all possible outcomes.
3) The sample space is represented using S.
4) A subset of the sample space of an experiment is called an event represented by E.

Complete step by step solution:
When two dice are thrown, we may get an outcome as (1, 1), (2, 5), (1, 6), (3, 1) etc.
Since, there are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:
$$\left(1,1\right),\left(1,2\right),\left(1,3\right),\left(1,4\right),\left(1,5\right),\left(1,6\right)=6possibilities.$$
$$\left(2,1\right),\left(2,2\right),\left(2,3\right),\left(2,4\right),\left(2,5\right),\left(2,6\right)=6possibilities.$$
$$\left(3,1\right),\left(3,2\right),\left(3,3\right),\left(3,4\right),\left(3,5\right),\left(3,6\right)=6possibilities.$$
$$\left(4,1\right),\left(4,2\right),\left(4,3\right),\left(4,4\right),\left(4,5\right),\left(4,6\right)=6possibilities.$$
$$\left(5,1\right),\left(5,2\right),\left(5,3\right),\left(5,4\right),\left(5,5\right),\left(5,6\right)=6possibilities.$$
$$\left(6,1\right),\left(6,2\right),\left(6,3\right),\left(6,4\right),\left(6,5\right),\left(6,6\right)=6possibilities.$$
Total number of elements (possibilities) of set S are therefore,$$n\left(S\right)=6\times 6=36$$; i.e. six possibilities of second dice for each of the six possibilities of the first dice.

Note:
1) A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set.
2) The probability of an outcome E in a sample space S is a number P between 1 and 0 that measures the likelihood that E will occur on a single trial.