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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∩M)=60276027+2147+4064+1313=602712551=0.44

05

Determine events are independent or not

P(W∩M)=P(W)×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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Most popular questions from this chapter

Management system failures. Refer to the Process Safety Progress (December 2004) study of 83 industrial accidents caused by management system failures, Exercise 2.150(p. 142). A summary of the root causes of these 83 incidents is reproduced in the following table. One of the 83 incidents is randomly selected and the root cause is determined.

Management system cause category

Number of incidents

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a. List the sample points for this problem and assign reasonable probabilities to them.

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In a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. One of the 106 social robots is randomly selected and the design (e.g., wheels only) is noted.

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A = {Adele 1, Adele 2, White Stripes 1, White Stripes 2, Maroon Five}

B = {Adele 2, White Stripes 1, Maroon Five, White Stripes 2, Adele 1}

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  4. Given that Adele 1, Adele 2, and White Stripes 1 are the first three songs selected, what is the probability that White Stripes 2 is selected as the fourth song to play from the playlist?
  5. Given that Adele 1, Adele 2, White Stripes 1 and White Stripes 2 are the first four songs selected, what is the probability that Maroon Five is selected as the last song to play from the playlist?
  6. Find the probability of List A by multiplying the probabilities in parts a–e.
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