Answer: Let's start by calculating the probability that an 18-year-old driver is involved in an accident:
P(accident) = 124/2000 = 0.062
Let's assume that the insurance company pays the full cost of the accident, which is $15,000. Then the expected cost of covering one 18-year-old driver is:
Expected cost = P(accident) x Cost of accident = 0.062 x $15,000 = $930
If the insurance company wants to make a 20% profit on policies, they need to charge a premium that covers their expected cost plus their desired profit. The premium, denoted by P, can be calculated as follows:
P = (Expected cost + Desired profit) / (1 - Profit margin)
where Profit margin is the percentage of the premium that represents the profit. In this case, Profit margin is 20%, or 0.20.
Substituting the values we have calculated, we get:
P = ($930 + 0.20 x $930) / (1 - 0.20)
= $1,236.00
Therefore, the insurance company should charge 18-year-old drivers a premium of $1,236.00 to make a 20% profit on policies.
Explanation: