Why might a commercial premium be higher than expected covered claims?

• To help cover running costs and uncertainty as well as claims
• To guarantee that every insured household files a claim each year
• To repay the full value of every insured asset each policy year

Over one year, a machine has a 1 in 50 chance of a 6,000-coin loss. Otherwise the loss is zero. What is the expected yearly loss, in coins?

How can a yearly premium be much smaller than the cost of rebuilding a home after a rare covered fire?

• The insurer lowers the size of every possible loss before it occurs
• Many premiums fund the covered losses suffered by a smaller group
• A large pool guarantees that all households avoid any loss that year

Buyers know their risk group, but an insurer cannot distinguish the groups. Both groups can buy the same voluntary cover at the same price. Which group may find it more attractive?

• The higher-risk group, because the shared price offers it more value
• The lower-risk group, because its smaller expected claims require more cover
• Both groups must join equally, because the policy price alone fixes demand

A policy has expected covered claims of 110 coins for one year and a yearly premium of 155 coins. How much of the premium is above expected claims?

• 110 coins above the expected yearly claim cost
• 155 coins above the expected yearly claim cost
• 45 coins above the expected yearly claim cost

A policy pays all of a covered 700-coin repair bill above a 100-coin per-claim deductible. There are no other charges or limits. How much does the insurer pay?

• 700 coins; the owner pays nothing from the covered loss
• 600 coins; the owner pays the first 100 coins
• 100 coins; the insurer pays only the deductible amount

A voluntary scheme raises its common premium. Some lower-risk drivers leave. No driver's own risk changes. Why can expected claims per member rise?

• Each departure raises the personal accident risk of every remaining driver
• Higher prices prove that all departing drivers were about to make claims
• Lower-risk departures raise expected claims per remaining member

Adding more insured homes in the same flood zone guarantees predictable average claims, even when one flood can damage them together.