The table shows the distribution, by age and gender, of the 30.6 million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person living alone in the region is male.

\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
& \begin{tabular}{l}
Ages \\
[tex]$18-24$[/tex]
\end{tabular}
& \begin{tabular}{c}
Ages \\
[tex]$25-34$[/tex]
\end{tabular}
& \begin{tabular}{l}
Ages \\
[tex]$35-44$[/tex]
\end{tabular}
& \begin{tabular}{l}
Ages \\
[tex]$45-64$[/tex]
\end{tabular}
& \begin{tabular}{l}
Ages \\
[tex]$65-74$[/tex]
\end{tabular}
& \begin{tabular}{l}
Ages \\
[tex]$75+$[/tex]
\end{tabular}
& Total \\
\hline
Male & 0.7 & 2.3 & 2.5 & 4.1 & 1.8 & 1.1 & 12.5 \\
\hline
Female & 0.6 & 1.7 & 1.7 & 6.0 & 2.7 & 5.4 & 18.1 \\
\hline
Total & 1.3 & 4.0 & 4.2 & 10.1 & 4.5 & 6.5 & 30.6 \\
\hline
\end{tabular}



Answer :

To find the probability that a randomly selected person living alone in the region is male, follow these steps:

1. Understand the Given Data:
- The table shows the distribution of people living alone in various age groups, separated by gender.
- The total number of people living alone in the region is 30.6 million.
- The total number of males living alone in the region is 12.5 million.

2. Recall the Formula for Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. In this case:
[tex]\[ \text{Probability} = \frac{\text{Number of males living alone}}{\text{Total number of people living alone}} \][/tex]

3. Plug in the Given Values:
We know:
- Number of males living alone = 12.5 million
- Total number of people living alone = 30.6 million
[tex]\[ \text{Probability of selecting a male} = \frac{12.5}{30.6} \][/tex]

4. Calculate the Probability:
Performing the division gives us the probability:
[tex]\[ \frac{12.5}{30.6} \approx 0.4085 \][/tex]

So, the probability that a randomly selected person living alone in the region is male is approximately [tex]\(0.4085\)[/tex] or [tex]\(40.85\%\)[/tex].