Home Warranties and Inspections - Radon found

I've sold my home contingent on a private inspection. Unfortunately the inspection found radon in my basement. I understand the acceptable level for radon is 4 and the reading in my basement was 8.2.
The buyers have requested that the radon be "defumigated" and an eradication/mitigation system be installed. Will installing the eradication/mitigation system also defumigate the radon that is already present or is a separate process required to defumigate the radon?
I have a state certified company installing a sub-slab/drain tile ventilation system with an alarm etc. for approx $800. Are these systems effective? The company said they guarantee a reading under 1.8 once the system is installed. Are there any issues or concerns with these systems that I should be aware of? Are there any specific questions I should be asking the installer regarding the system? Any other thoughts, info. or advice regarding eradication or defumigation of radon would be appreciated.
As always thanks for your help!!

Your State Radiation Control Agency (Environmental Quality or Health Dept) has free literature about radon in homes. EPA also has free literature. Both will include mitigation techniques and concerns you might have. Contact them. The reductions you mention should address any concerns you have. Radon-222 is continously generated from soils containing Radium-226 which is found throughout soils on this planet.

All your questions are answered here: http://radonworld.com/reduce.htm