Problem

The table shows the distribution, by age and gender, of the 29.8 million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 25-34 age range. \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline & $\begin{array}{l}\text { Ages } \\ 18-24\end{array}$ & $\begin{array}{l}\text { Ages } \\ 25-34\end{array}$ & $\begin{array}{l}\text { Ages } \\ 35-44\end{array}$ & $\begin{array}{l}\text { Ages } \\ 45-64\end{array}$ & $\begin{array}{l}\text { Ages } \\ 65-74\end{array}$ & $\begin{array}{l}\text { Ages } \\ \geq 75\end{array}$ & Total \\ \hline Male & 0.8 & 2.6 & 2.5 & 4.9 & 1.6 & 1.9 & 14.3 \\ \hline Female & 0.7 & 1.8 & 1.8 & 4.0 & 2.4 & 4.8 & 15.5 \\ \hline Total & 1.5 & 4.4 & 4.3 & 8.9 & 4.0 & 6.7 & 29.8 \\ \hline \end{tabular} The probability is (Type an integer or decimal rounded to the nearest hundredth as needed.)

Solution

Step 1 :The question is asking for the probability that a randomly selected person living alone in the region is in the 25-34 age range. From the table, we can see that there are 4.4 million people in the 25-34 age range. The total number of people living alone in the region is 29.8 million.

Step 2 :So, the probability would be the number of people in the 25-34 age range divided by the total number of people living alone in the region.

Step 3 :Let's denote the total number of people as \(T\) and the number of people in the 25-34 age range as \(P\). So, \(T = 29.8\) million and \(P = 4.4\) million.

Step 4 :The probability \(Pr\) can be calculated as \(Pr = \frac{P}{T}\).

Step 5 :Substituting the values, we get \(Pr = \frac{4.4}{29.8} = 0.1476510067114094\).

Step 6 :Rounding to the nearest hundredth, we get \(Pr = 0.15\).

Step 7 :Final Answer: The probability that a randomly selected person living alone in the region is in the 25-34 age range is approximately \(\boxed{0.15}\).

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Source: https://solvelyapp.com/problems/16503/

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