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PROBABILITY — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsPROBABILITY3 Marks
Question
Two six faced balanced dice are thrown simultaneously. State the sample space of this random experiment and hence write the sets showing the following events :
$(1)$ Event $=$ The sum of numbers on the dice is $7.$
$(2)$ Event $=$ The sum of numbers on the dice is less than $4.$
$(3)$ Event $=$ The sum of numbers on the dice is divisible by $3.$
$(4)$ Event $=$ The sum of numbers on the dice is more than $12.$
✓

Answer

The sample space for throwing two six faced balanced dice simultaneously is as follows:  
$U = \{(1,1); (1,2); (1,3); (1,4); (1,5); (1,6)$  
  $(2,1); (2,2); (2,3); (2,4); (2,5); (2,6)$
  $(3,1); (3,2); (3,3); (3,4); (3,5); (3,6)$  
  $(4,1); (4,2); (4,3); (4,4); (4,5); (4,6)$  
  $(5,1); (5,2); (5,3); (5,4); (5,5); (5,6)$  
  $(6,1); (6,2); (6,3); (6,4); (6,5); (6,6)\}$  
$(1)$ Event $=$ The sum of numbers on the dice $=$ is $7.$  
  $= \{(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)\}$  
$(2)$ Event $=$ The sum of numbers on the dice is less than $4.$  
  $= \{(1,1), (1,2), (2,1)\}$  
$(3)$ Event $=$ The sum of numbers on the dice is divisible by $3.$  
  $= \{(1,2), (1,5), (2,1), (2,4), (3,3), (3,6), (4,2), (4,5), (5,1), (5,4), (6,3), (6,6)\}$  
$(4)$ Event $=$ The sum of numbers on the dice is more than $12.$  
  $= \{\ \}$ OR   

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