Final answer:
A group of 100 drivers, each paying an annual premium of $1,860, allows an insurance company to collect $186,000. This equals the total damage from car accidents incurred by the group through minor, medium, and major incidents combining to the same amount.
Step-by-step explanation:
Total Damage Calculation for Car Accidents
A simplified example of automobile insurance might work this way: Imagine we have a pool of 100 drivers who are all insured and cannot be categorized as low-risk, medium-risk, or high-risk at the start of the year. During that year, 60 drivers incur minor dents and dings that cost $100 each to repair. Another 30 drivers are involved in moderate accidents that result in $1,000 in damages per accident. Lastly, 10 drivers experience significant accidents, with each accident leading to $15,000 in damages.
To calculate the total damage from these accidents, we multiply the number of incidents in each risk group by the cost per incident. We then sum these amounts:
60 minor incidents x $100 each = $6,000
30 medium incidents x $1,000 each = $30,000
10 major incidents x $15,000 each = $150,000
So, the total damage incurred by car accidents in this group is $6,000 (minor) + $30,000 (medium) + $150,000 (major) = $186,000.
If each driver pays an annual premium of $1,860, the insurance company collects 100 drivers x $1,860 = $186,000, which equals the total damage incurred. This is how automobile insurance companies can pool the risks and ensure that enough funds are collected to cover the costs of accidents across their policyholders.