solution

 

. It is common for governments to gather data on family structure in the population. Information on family structure distribution is important because of the known associations between family structure and child well-being, behavior, and general success in life. Additionally, information on family structure in the population has business implications for such things as day care for employees and location of work (for example, from home or at organization). Here are data from 2006 on Canadian families with at least one child:17

$1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn$1rn Common-

$1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn   Married$1rn$1rn law$1rn  Mother$1rn$1rn Father

Number of children$1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn couple$1rn  couple$1rn  only$1rn $1rn    only

One child at home$1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn 1,267,625   291,255    682,025$1rn   188,790

Two children at home$1rn $1rn $1rn $1rn $1rn $1rn $1rn$1rn 1,497,755   234,755$1rn 327,660$1rn   72,655

Three or more children

at home$1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn $1rn  678,405$1rn   92,140$1rn   122,605$1rn   20,320

(a) What is the probability that a randomly chosen family with at least one child is a single-parent family?

(b) If you know that the family chosen is a married couple, what is the conditional probability that the family has two children?

(c) Are the events “mother-only family” and “one child at home” independent? How do you know?