An insurance company issues a policy on a small boat under the following conditions: • The replacement cost ($5000) will be paid for a total loss.
• If it is not a total loss, but the damage is more than $2000, then $1500 will be
paid.
• Nothing will be paid for damage costing $2000 or less.
• Nothing is paid out if there is no damage.
The company estimates the probability of the first three events as .02, 10, and .30
respectively. The amount the company should charge if it wishes to make a profit of
$50 above the expected amount paid out in a year is: