How does the problem of Adverse Selection affects the insurance sector?

Suppose that an insurance company provides insurance against car accidents. It does a survey and finds that there are some areas with higher chances of accidents and some areas with lower chances of accidents but does not know with certainty about exactly which are the accident prone areas. In this case, the insurance company might decide to fix insurance premium based on the average rate.
Then, the most expected result of this situation will be that insurance company will soon go broke. This is because the people who drive in accident prone areas will be keener on seeking the insurance because the price of insurance that they will have to pay will be lesser than their loss. So, there will be more chances of an insurance claim being made which will bring huge losses to the company. Thus, the company suffers problems because of the adverse selection. Had it known with certainty about which are the accident prone areas, it would not have given insurance to drivers in that area at the average rate.