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Chapter 3: Q72E (page 196)

Working mothers with children. The U.S. Census Bureaureports a growth in the percentage of mothers in the workforce who have infant children. The following table gives a breakdown of the marital status and working status of mothers with infant children in the year 2014. (The numbers in the table are reported in thousands.) Consider the following events: A = {Mom with infant works}, B = {Mom with infant is married}. Are A and B independent events?

working

Not working

Married

6027

4064

No spouse

2147

1313

(Data from U.S. Census Bureau, Bureau of LabourStatistics, 2014 (Table 4).

Short Answer

Expert verified

The probability of W working mother with young children is0.60.

TheProbability of M married mother with young children is 0.75

The events are not independent.

Step by step solution

01

Given information

According to the information,the US census table,the marital statues and occupational situation of mothers with young children in 2014.

W=working mother having young children

M=married mother with young children.

The formula for probability is P=favourableoutcomestotaloutcomes

02

Step 2:The probability of W working mother with young children 

The probability is

P(W)=6027+21476027+2147+4064+1313=817413551=0.60

03

Step 3: Probability of M married mother with young children

P(M)=6027+40646027+2147+4064+1313=1009113551=0.75

04

The probability of P(W∩M) 

P(W鈭�M)=60276027+2147+4064+1313=602712551=0.44

05

Determine events are independent or not

P(W鈭�M)=P(W)脳P(M)=(0.60)(0.75)=0.45

Thus event is not independent.

Therefore

The probability of W working mother with young children is0.60.

TheProbability of M married mother with young children is 0.75

The events are not independent.

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