The perfect cube numbers are in given set
{1,2,3,4,......,100} are
1,8,27,64,125,216 343,512,729,1000 and the natural numbers having odd number of division are perfect square numbers and the perfect square numbers in given set are
1,4,9,16,25,36,49,64,81,100,121,144, 169,196,225,256,289,324,361,400,441,484, 529,576,625,676,729,784,841,900,961.
So required probability is
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