Probabilty Please help and explain in detail how you came to the answer

Question

According to Statistics Norway, there are a total of 1,079,641 mothers among Norwegian women born 1935-1991. Among these, 860209 have at least two children, 368 445 have at least three children, and 95 993 have at least four children. If you pick a random mother among these, what is the probability that she has two or three children?

Answer 1

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%).