The idea of insurance is that we all face risks that are unlikely to be realized but carry high costs. Worker's compensation insurance provides for the cost of medical care, rehabilitation, and other related expenses for injured workers. In a given year, most workers will not have any work injury, some will have minor injuries, and a few will die or become permanently disabled. Insurance spreads the risk: We all pay a small amount, and the insurance policy pays a large amount to these few extreme claims. The National Academy of Social Insurance reports that the mean worker's compensation claim cost in a year is $=$$$439$ per covered worker. An insurance company plans to sell worker's compensation insurance for $$439$ plus enough to cover its administrative costs and profit.

Choose the correct explanation for why it would be unwise to sell only $12$ policies.

$$439$ does not even cover the cost of an emergency room visit, so even if an accident were work$-$related, the employee should use their personal insurapce.

Although the probability of having to pay worker's compensation for one or more of the $12$ policies is very small, if this were to happen, it could be financially disastrous.

The probability of having to pay worker's compensation for one or more of the $12$ policies is very high and if this were to happen it could be financially disastrous.

The income from the $12$ policies would not cover the salary of the insurance agent, so it would not be worth running the program.