Two dice are rolled write the sample space

Answer

Verified

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:\[\left( {1,{\text{ }}1} \right),{\text{ }}\left( {1,{\text{ }}2} \right),{\text{ }}\left( {1,{\text{ }}3} \right),{\text{ }}\left( {1,{\text{ }}4} \right),{\text{ }}\left( {1,{\text{ }}5} \right),{\text{ }}\left( {1,{\text{ }}6} \right){\text{ }} = {\text{ }}6{\text{ }}possibilities.\]\[\left( {2,{\text{ }}1} \right),{\text{ }}\left( {2,{\text{ }}2} \right),{\text{ }}\left( {2,{\text{ }}3} \right),{\text{ }}\left( {2,{\text{ }}4} \right),{\text{ }}\left( {2,{\text{ }}5} \right),{\text{ }}\left( {2,{\text{ }}6} \right){\text{ }} = {\text{ }}6{\text{ }}possibilities.\]\[\left( {3,{\text{ }}1} \right),{\text{ }}\left( {3,{\text{ }}2} \right),{\text{ }}\left( {3,{\text{ }}3} \right),{\text{ }}\left( {3,{\text{ }}4} \right),{\text{ }}\left( {3,{\text{ }}5} \right),{\text{ }}\left( {3,{\text{ }}6} \right){\text{ }} = {\text{ }}6{\text{ }}possibilities.\]\[\;\left( {4,{\text{ }}1} \right),{\text{ }}\left( {4,{\text{ }}2} \right),{\text{ }}\left( {4,{\text{ }}3} \right),{\text{ }}\left( {4,{\text{ }}4} \right),{\text{ }}\left( {4,{\text{ }}5} \right),{\text{ }}\left( {4,{\text{ }}6} \right){\text{ }} = {\text{ }}6{\text{ }}possibilities.\]\[\;\left( {5,{\text{ }}1} \right),{\text{ }}\left( {5,{\text{ }}2} \right),{\text{ }}\left( {5,{\text{ }}3} \right),{\text{ }}\left( {5,{\text{ }}4} \right),{\text{ }}\left( {5,{\text{ }}5} \right),{\text{ }}\left( {5,{\text{ }}6} \right){\text{ }} = {\text{ }}6{\text{ }}possibilities.\]\[\;\left( {6,{\text{ }}1} \right),{\text{ }}\left( {6,{\text{ }}2} \right),{\text{ }}\left( {6,{\text{ }}3} \right),{\text{ }}\left( {6,{\text{ }}4} \right),{\text{ }}\left( {6,{\text{ }}5} \right),{\text{ }}\left( {6,{\text{ }}6} \right){\text{ }} = {\text{ }}6{\text{ }}possibilities.\]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.

When two dices are thrown, there are (6 × 6) = 36 outcomes.The set of these outcomes is the sample space, which is given by

S = (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)