Q. 44.4( 40 Votes )

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Answer :

Given: n(A) = 130, n(B) = 180 and n (A B) = x = 110

Total number of students = 220


n(A) = number of students whose hobby is rock climbing


n(B) = number of students whose hobby is sky watching


n (A B) = number of students whose hobby is both


n (A B) = number of students whose hobby is either rock climbing or sky watching


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As we know, n (A B) = n(A) + n(B) - n (A B)


n (A B) = 130 + 180 - 110


n (A B) = 310 - 110


n (A B) = 200


Then,


(i) The number of students who do not have any of the two hobbies


= 220– 200


= 20


(ii) The number of students whose hobby is rock climbing


= 130– 110


= 20


(iii) The number of students whose hobby is sky watching


= 180– 110


= 70


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