If you consider two different types of consumer, with high probability to claim or ill and another type of consumer with lower probability of illness, then certainly the p is different.  Then if the consumer is observable. Then the insurance will based on the two types' utility curve and the company' insurance level. If the type is unobservable, as you have the condition, the company will choose a insurance level to try to attract both type but not trap into a loss as there is always the problem of moral hazard. Hope this help.