Insurance is basically a game of profiling. The entire concept of insurance starts from a basis of a large, single class of people who cooperate to distribute the costs of improbable incidents over the group. Insurance companies don't treat everyone as one large, single class though. They break people down by age, gender, miles driven on average, geographic region, and tons of other metrics that are used to assess your risk level. Higher risk level? Hire risk class. Higher premium.

Also, you're not really insuring yourself. At least not in the way you think. In most cases, you're insuring yourself against liability, which means you're really insuring the other guy. If you get in to an accident, your insurance pays the other guy's medical bills, not yours. You can usually get some small amount of coverage for yourself, but it's a fraction of the liability coverage.