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The table shows the number of people in a certain country who moved in 2004, expressed in millions, categorized by where they moved and whether they were an owner or a renter.

\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
Moved to \\
Same \\
Region
\end{tabular} & \begin{tabular}{c}
Moved to \\
Different \\
Region
\end{tabular} & \begin{tabular}{c}
Moved to \\
Different \\
Country
\end{tabular} \\
\hline Owner & 11.6 & 2.9 & 0.3 \\
\hline Renter & 18.7 & 4.5 & 1.0 \\
\hline
\end{tabular}

Find the probability, expressed as a decimal rounded to the nearest hundredth, that a randomly selected citizen who moved in 2004 was an owner.

[tex]$P($[/tex] citizen was an owner [tex]$) \approx$[/tex] [tex]$\square$[/tex]

(Round to the nearest hundredth as needed.)



Answer :

GinnyAnswer
Let's solve the problem step-by-step.

1. Identify the number of people who moved:

We have been given the following data:

- Owners:
- Moved to Same Region = 11.6 million
- Moved to Different Region = 2.9 million
- Moved to Different Country = 0.3 million

- Renters:
- Moved to Same Region = 18.7 million
- Moved to Different Region = 4.5 million
- Moved to Different Country = 1.0 million

2. Calculate the total number of owners who moved:

[tex]\[ \text{Total Owners} = 11.6 + 2.9 + 0.3 = 14.8 \text{ million} \][/tex]

3. Calculate the total number of renters who moved:

[tex]\[ \text{Total Renters} = 18.7 + 4.5 + 1.0 = 24.2 \text{ million} \][/tex]

4. Calculate the total number of people who moved (owners and renters combined):

[tex]\[ \text{Total Number of People Who Moved} = 14.8 + 24.2 = 39.0 \text{ million} \][/tex]

5. Calculate the probability that a randomly selected citizen who moved was an owner:

[tex]\[ P(\text{Owner}) = \frac{\text{Total Number of Owners}}{\text{Total Number of People Who Moved}} = \frac{14.8}{39.0} \][/tex]

Using the division:

[tex]\[ P(\text{Owner}) \approx 0.3794871794871795 \][/tex]

6. Round the probability to the nearest hundredth:

[tex]\[ P(\text{Owner}) \approx 0.38 \][/tex]

Therefore, the probability that a randomly selected citizen who moved in 2004 was an owner is approximately [tex]\( 0.38 \)[/tex].

So, the final answer is:

[tex]\[ P (\text{citizen was an owner}) \approx 0.38 \][/tex]

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