☼ Sample  Space     :     A set representing all possible outcomes of a random experiment is called a sample space and it is denoted by  S  or  U.

Each outcome is called a sample point. The number of sample points in S may be denoted  by  n(S). If the number of sample points of S is finite, it is known as a finite sample space and if the number of sample points is infinite, it is known as an infinite sample space.

e.g. (i) If a coin is tossed, the sample space will be as follows :

S = {H, T}

(ii) If two coins are tossed the following sample space is generated:

S = { HH, HT, TH, TT }

(iii) If  3 coins are thrown simultaneously, the sample space is given by :

S = { HHH, HHT, HTH, THH, TTH, THT, HTT, TTT }

(iv) If two dice are thrown the following sample space is obtained 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) }

=    { ( i, j )  /   i, j =  1, 2, 3, 4, 5, 6   }

(v) If a coin is tossed until head appears,  we get the following sample space

S  =  {H, TH, TTH, TTTH, TTTTH, . . . }

     In the first four experiments the sample spaces are finite while in the fifth experiment the sample space is an  infinite

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