Answer :

Since a pair of dice is thrown, all the possible outcomes or sample space (S) will be as follows


A: the sum is greater than 8


Possible sum greater than 8 are 9, 10, 11 & 12


A=


B: 2 occurs on either die


Here possibilities are there that the number 2 will come on first die or second die or both the die simultaneously


B=


C: The sum is at least 7 and multiple of 3


So the sum can be only 9 or 12


C=


For 2 elements to be mutually exclusive, then there should not be any common element amongst them


(i) A B =ϕ


As there is no common element in A and B


So A& B are mutually exclusive


(ii) B C = ϕ


Since there is no common element between


So B and C are mutually exclusive.


(iii) A C


ϕ


Since A and C has common elements,


A and C are mutually exclusive.


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