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Assume that the probability of a given driver getting into an accident is 10%,
the average cost of an accident is [tex]$18,300, and the overhead cost for an
insurance company per insured driver is $[/tex]110. What should be this driver's
annual insurance premium?
OA. [tex]$2634
○ B. $[/tex]1830
O C. [tex]$1940
○ D. $[/tex]2534

Sagot :

GinnyAnswer
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 \( C. \$[/tex]1940 \).
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