Answered

Among the licensed drivers in the same age group, what is the probability that a 23-year-old was involved in an accident? Use the table below.

\begin{tabular}{|l|l|l|l|}
\hline
Age group & \begin{tabular}{l}
Drivers in \\
accidents \\
(thousands)
\end{tabular} & \begin{tabular}{l}
Drivers in \\
fatal \\
accidents
\end{tabular} & \begin{tabular}{l}
Licensed \\
drivers \\
(thousands)
\end{tabular} \\
\hline
19 and under & 2,150 & 5,400 & 10,034 \\
\hline
[tex]$20-24$[/tex] & 2,620 & 8,700 & 17,173 \\
\hline
[tex]$25-34$[/tex] & 3,740 & 10,700 & 35,712 \\
\hline
[tex]$35-44$[/tex] & 3,220 & 9,600 & 40,322 \\
\hline
[tex]$45-54$[/tex] & 3,030 & 9,400 & 40,937 \\
\hline
[tex]$55-64$[/tex] & 1,990 & 6,500 & 30,355 \\
\hline
[tex]$65-74$[/tex] & 790 & 3,800 & 17,246 \\
\hline
75 and over & 560 & 4,300 & 13,321 \\
\hline
\end{tabular}

A. [tex]$15.8\%$[/tex]
B. [tex]$16.5\%$[/tex]
C. [tex]$17.3\%$[/tex]
D. [tex]$15.3\%$[/tex]



Answer :

GinnyAnswer
To find the probability that a licensed driver aged 23 was involved in an accident, we'll use the data provided for the age group 20-24 since 23 falls within this range. Here is the step-by-step solution:

1. Identify the relevant data:
- For the age group 20-24:
- Drivers in accidents: 2620 thousand
- Licensed drivers: 17173 thousand

2. Calculate the probability:
- The probability is obtained by dividing the number of drivers in accidents by the total number of licensed drivers in the same age group and then multiplying by 100 to convert it into a percentage:
[tex]\[ \text{Probability} = \left( \frac{\text{Drivers in accidents}}{\text{Licensed drivers}} \right) \times 100 \][/tex]
- Substitute the given values:
[tex]\[ \text{Probability} = \left( \frac{2620}{17173} \right) \times 100 \][/tex]
- Performing this calculation gives:
[tex]\[ \text{Probability} \approx 15.256507307983464 \% \][/tex]

3. Compare with the provided choices:
- The choices provided are:
- A. 15.8 %
- B. 16.5 %
- C. 17.3 %
- D. 15.3 %
- The closest matching choice to 15.256507307983464 % is 15.3 %.

Therefore, the most accurate probability that a licensed driver aged 23 was involved in an accident is approximately 15.3 %, which corresponds to option D.

So, the correct answer is:
D. 15.3 %