"+" is the wrong mathematical operation for combining fractions of distinct sets. The right operation is a weighted sum: 1/3×1/2 + 1/3×1/2 = 1/3 The "1/2" is

"+" is the wrong mathematical operation for combining fractions of distinct sets. The right operation is a weighted sum: 1/3×1/2 + 1/3×1/2 = 1/3 The "1/2" is there because each of the two sets that we are combining is the same size.