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

Total mothers=1079641=A+B+C+D.

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.

860209=B+C+D,

368445=C+D,

95993=D.

C=368445-95993=272452, B=860209-368445=491764.

A=1079641-860209=219432.

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%).