To determine the driver's annual insurance premium, we need to calculate the expected cost due to accidents and then add the overhead cost to that.
Let's break down the calculations step-by-step:
1. Determine the probability and average cost of an accident:
- Probability of a given driver getting into an accident (accident_prob) = 10% = 0.10
- Average cost of an accident (avg_accident_cost) = [tex]$18,300
2. Calculate the expected cost due to accidents:
- The expected cost due to accidents is found by multiplying the probability of an accident by the average cost of an accident.
- Expected accident cost = accident_prob * avg_accident_cost
- Expected accident cost = 0.10 * 18,300 = 1,830
3. Add the overhead cost:
- The overhead cost for the insurance company per insured driver (overhead_cost) = $[/tex]110
- Total insurance premium = Expected accident cost + Overhead cost
- Total insurance premium = 1,830 + 110 = 1,940
4. Choose the closest option:
- From the given options: [tex]$2634, $[/tex]1830, [tex]$1940, and $[/tex]2534, the one that matches our calculated insurance premium is [tex]$1940.
Therefore, the driver's annual insurance premium should be \( C. \$[/tex]1940 \).
