The company estimates the probability of no damage to be 0.60, the probability of damage between $0 and $10,000 to be 0.25, and the probability of damage between $10,000 and $25,000 to be 0.12. If the company wants to make a profit of $200 above the expected cost, what should be the price of the policy?
To calculate the price of the policy, we need to consider the expected cost of damages and add the desired profit of $200.
First, let's calculate the expected cost of damages. We need to multiply the probability of each range of damages by the cost of that range and then sum up the results.
1. The probability of no damage is 0.60, and the cost for no damage is $0.
Expected cost of no damage = 0.60 * $0 = $0
2. The probability of damage between $0 and $10,000 is 0.25, and the cost for that range is between $0 and $10,000.
Expected cost of damage between $0 and $10,000 = 0.25 * ($0 to $10,000)
3. The probability of damage between $10,000 and $25,000 is 0.12, and the cost for that range is between $10,000 and $25,000.
Expected cost of damage between $10,000 and $25,000 = 0.12 * ($10,000 to $25,000)
To find the expected cost for the second and third ranges, we need to find the average cost for each range. Let's assume the average cost for the second range is $5,000 and for the third range is $17,500.
Expected cost of damage between $0 and $10,000 = 0.25 * $5,000 = $1,250
Expected cost of damage between $10,000 and $25,000 = 0.12 * $17,500 = $2,100
Now, let's calculate the total expected cost of damages by summing up these expected costs:
Total expected cost of damages = $0 + $1,250 + $2,100 = $3,350
Finally, add the desired $200 profit to the total expected cost to get the price of the policy:
Price of the policy = Total expected cost + Desired profit = $3,350 + $200 = $3,550
Therefore, the price of the policy should be $3,550.