Let's divide the mothers into specific groups:
A: Mothers having one child
B: Mothers having two children
C: Mothers having three children
D: Mothers having four or more children
Note that we are given the total number of mothers, not women, so we can deduce that no childless women are included.
D includes A+B+C, C includes A+B, B includes A.
The number of mothers with exactly two or three children=B+C=491764+272452=764216. This excludes mothers with four or more children.
The required probability is therefore 764216/1079641=0.7078 approx (70.78%).