Question

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

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

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 $\mathbf{P}\mathbf{=}\frac{\mathbf{favourableoutcomes}}{\mathbf{totaloutcomes}}$

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

The probability is

$\begin{array}{rcl}P\left(W\right)& =& \frac{6027+2147}{6027+2147+4064+1313}\\ & =& \frac{8174}{13551}\\ & =& 0.60\\ & & \end{array}$

Step 3: Probability of M married mother with young children

$\begin{array}{rcl}P\left(M\right)& =& \frac{6027+4064}{6027+2147+4064+1313}\\ & =& \frac{10091}{13551}\\ & =& 0.75\\ & & \end{array}$

The probability of P(W∩M) 

$\begin{array}{rcl}P(W\cap M)& =& \frac{6027}{6027+2147+4064+1313}\\ & =& \frac{6027}{12551}\\ & =& 0.44\\ & & \end{array}$

Determine events are independent or not

$\begin{array}{rcl}P(W\cap M)& =& P\left(W\right)\times P\left(M\right)\\ & =& (0.60)(0.75)\\ & =& 0.45\\ & & \end{array}$

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.