What is the purpose of purchasing auto insurance?

Just like any other insurance the purpose is to transfer your risk of loss to the insurance company. The company is merely like a large co-op. It is almost impossible when you will have an accident and how much the damages will cost. However, when you have a large number of people, a company can make estimates on how many will have accidents and how much the damages will pay out. This is done by the law of large numbers. The company takes your unknown risk and replaces it with a know certainty. The know amount is the premiums you pay and the unknown risk of when you will have an accident and how much it might cost.