Problem

The table shows the distribution, by age and gender, of the 30.1 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 \\ $18-24$ \end{tabular} & \begin{tabular}{l} Ages \\ $25-34$ \end{tabular} & \begin{tabular}{l} Ages \\ $35-44$ \end{tabular} & \begin{tabular}{l} Ages \\ $45-64$ \end{tabular} & \begin{tabular}{l} Ages \\ $65-74$ \end{tabular} & \begin{tabular}{c} Ages \\ 275 \end{tabular} & Total \\ \hline Male & 0.7 & 29 & 2.8 & 4.8 & 1.5 & 1.4 & 14.1 \\ \hline Female & 0.8 & 1.3 & 1.7 & 5.0 & 27 & 4.5 & 16.0 \\ \hline Total & 1.5 & 4.2 & 4.5 & 9.8 & 42 & 5.9 & 30.1 \\ \hline \end{tabular} The probability is $\square$ (Type an integer or decimal rounded to the nearest hundredth as needed)

Solution

Step 1 :The problem provides a table that shows the distribution, by age and gender, of the 30.1 million people in a certain region who live alone.

Step 2 :We are asked to find the probability that a randomly selected person living alone in the region is male.

Step 3 :From the table, we can see that the total number of males living alone is 14.1 million.

Step 4 :The total population of people living alone is 30.1 million.

Step 5 :The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. In this case, the event is selecting a male, and the total number of outcomes is the total population.

Step 6 :So, the probability that a randomly selected person living alone in the region is male is calculated as follows: \(\frac{14.1}{30.1}\).

Step 7 :Calculating the above expression gives approximately 0.46843853820598.

Step 8 :Rounding to the nearest hundredth, we get \(\boxed{0.47}\).

Step 9 :So, the probability that a randomly selected person living alone in the region is male is approximately \(\boxed{0.47}\).

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