Illustration : 1
            A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be 
            (i) white ?                  (ii) blue ?            (iii) Red ?

Solution :
            Saying that a marble is drawn at random is a short way of saying that all the marbles are equally likely to be drawn. 
            Therefore, the number of possible outcomes = 3 + 2 + 4 = 9
            Let W denote the event ‘the marble is white’ , B denotes the event ‘the marble is blue’ and R denote the event ‘marble is red’.

Illustration : 2
       Two coins are tossed simultaneously. Find the probability of getting 
       (i) two heads        (ii) at least one head        (iii) no head. 
 Solution : 
       Let H denotes head and T denotes tail. 
       On tossing two coins simultaneously, all possible outcomes HH, HT, TH, TT = 4.

Illustration : 3
17 cards numbered 1, 2, 3, ........, 17 are put in a box and mixed throughly. One person draws a card from the box. Find the probability that the number on the card is 
 (i) odd        (ii) a prime    (iii) divisible by 3    (iv) divisible by 3 and 2 both. 
Solution :     
  (i) There are 9 odd numbered cards, namely 1, 3, 5, 7, 9, 11, 13, 15, 17. Out of these 9 cards one card can be drawn in 9 ways. 
      Favourable number of elementary events = 9
      Total number of elementary events = 17. 

(ii)     There are 7 prime numbered cards, namely. 2, 3, 5, 7, 11, 13, 17. Out of these 7 cards one card can be chosen in 7 ways.
         Favourable number of elementary events = 7 
         Total number of elementary events = 17

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(iv)     If a number is divisible by both 3 and 2, then it is a multiple of 6. In cards bearing  number 1, 2, 3, ........17 there are only 2 cards which bear a number divisible by 3 and 2  both i.e., by 6.  These cards bear numbers 6 and 12. 
          Favourable number of elementary events = 2