solution

If 1 in 50 people gets cancer, the cost of a policy would be about one-fiftieth of the cost of medical care in a competitive market. If the probability is 1 in 100 for nonsmokers and 1 in 10 for smokers, and smokers know this, then insurance would become much more attractive for smokers; there would be an adverse selection of smokers. Firms would find that they have to pay out on more than 1 in 50 policies, and the price would rise. In the limit, the price would rise to one-tenth the cost of medical care, and only smokers would purchase insurance.