How can an insurance company offer people a deal worth taking? Why do both the buyers and the sellers of insurance gain?

What will be an ideal response?

Insurance companies work by pooling risks so that everyone pays into the pool but only the (small) fraction of people who suffer a loss are paid from the pool. Although the likelihood of a bad occurrence is small for each individual, for a large enough group the total number and total amount of losses can be estimated very closely. The insurance company can calculate the size of the pool required to cover losses. From this calculation the company can compute the amount of the premium each person must pay into the pool to cover all the anticipated losses and other costs the company incurs. People buy insurance because they are risk averse; they want to avoid unwanted outcomes. Insurance is worth buying because people are willing to give up a relatively small amount of income all the time to guarantee that they do not face the uncommon occurrence of having to give up a large amount of income since this deal increases their expected utility. An insurance company will always try to take in more in premiums paid than claims paid out to claimants so that their owners receive at minimum a normal profit.