Page 98 - Mathematics Class - XI

2. If a die is thrown twice, the sample space is

 (, ),(, ),(, ),(, ),(, ),(, )11 12 13 14 15 16 
 
2 5),(,
 (, ),(, ),(, ),(,21 22 23 244),(, 2 6) 
 (, 33 34),(, ),(,
35 36),(, ) 
31 32),(, ),(,
S =  
41 4),(,,),( ,),( ,),( ,),( ,)2
 (, 4 34 4 4 5 4 6 
 (, ),(, ),(, ),(, ),(, ),51 52 53 54 55 ((, )56 
  
 (, ),(, ),(, ),(, ),(, ),(, )61 62 63 64 65 66 

Fig. (b)

Number of elements in S = 36 = 6 and so on.
2

OBSERVATION

1. Number of elements in sample space, when a die is thrown once = 6 = 6 1
2. Number of elements in sample space, when a die is thrown twice = 36 = 6 2

3. Number of elements in sample space, when a die is thrown thrice = 216 = 6 3

CONCLUSION

This activity concludes the number of elements in a sample space, when a die is thrown once, twice, thrice...

APPLICATION
This activity is useful in determining the probabilities of different events associated with the sample space.

Knowledge Booster
● If A and B are any two events, then P(A∪B) = P(A) + P(B) – P(A∩B)
● If A and B are mutually exclusive, then P(A∪B) = P(A) + P(B)

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