# Sample Space

ProbabilityBasicsVocabularyFormula → Sample Space

Sample space is the set of all possible outcomes of a random experiment. Following are some examples of the sample space (S.S).

Example 1. A coin is tossed only once.

$S.S=\{head, tail\}$

or simply,

$S.S=\{H,T\}$

Example 2. A coin is tossed two times. Or, two coins are tossed once.

$S.S=\{HH,HT,TH,TT\}$

Example 3. A dice is rolled once.

$S.S=\{1,2,3,4,5,6\}$

Example 4. A dice is rolled twice. Or, two dices are rolled once.

$S.S= \newline \Big\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \newline (2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \newline (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \newline (4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \newline (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \newline (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\Big\}$

Example 5. A football match is played.

In a football match between two teams A and B, what could be the possible outcomes? May be team A wins the match or may be team B. And, it is also possible that the match tie (or draw). So, the sample space is

$S.S=\{win, loss, equal\}$

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