When I bought my house ~3 years ago it failed Radon testing. I had the old homeowner reduce the cost of the house so that I could pay somebody to install a system. Then I never installed one.
I see a lot of people (ESPECIALLY REALTORS) extremely worried about the Radon risk. I am not a conspiracy theorist, but I think is is POSSIBLE that the risk is over-hyped. I have (a few years back) tried to find actual data relating to radon risks, but almost everything I found was a Meta-Analysis of the same few studies. One of the most commonly cited studies was a small number of miners who were working in mines with astronomically high levels of radon exposure, for extended periods of time developing cancer. For that study, IF radon were the culprit it was at levels so absurd that they'd practically never be seen in a home. But again, they were miners, and radon was likely not the only risk they had. In a couple (all but one I think?) of the other studies if you actually read them, they agreed that at very, very high levels there is a positive cancer correlation, but at low levels (order of magnitude seen in most homes regardless of mitigation) they found a NEGATIVE CORRELATION with cancer and radon.
Now it's been years since I have looked this up. Maybe there's more studies now, I don't know, but when the radon testing contractor tried to tell me that Radon was the #2 cause of lung cancer in the US and was an extremely dangerous carcinogen, I almost threw him out of the house. First, scaring me into purchasing anything ALWAYS pisses me off. (He conveniently did radon testing AND mitigation...) Second, when the #1 cause of cancer is orders of magnitude higher than everything else and (due to 2nd hand smoke) has the ability to cause cancer in non-smokers, almost everything else rapidly becomes statistical noise.
In short, if you're on this board you probably already question conventional wisdom of some things, and the current radon fears are something I urge you to question. Having said that, if you have the money, (or young kids) the systems are relatively cheap for the peace of mind they can offer. They are quiet, non-intrusive, and extremely inexpensive to operate. In my case, we'll be installing a system as a house sale may be pending, and potential buyers will want a system.
Look up some information for yourself, and if nothing else, you can use that information to leverage some extra money out of a seller. I firmly believe knowledge is power, and "finding" radon in a home after a purchase and sales is signed, will give you negotiating power. (BTW you can tell from homes in the area if there is a high probability of radon being an issue. Yes it's different from house to house, but neighborhoods and states trend towards different radon levels). Also note that older homes have different sub-slab preparation than newer homes and systems for older homes may be more costly to install.
https://www.google.com/url?url=https://www.aarst.org/proceedings/1988/1988_06_Correlation_Between_Mean_Radon_Levels_Lung_Cancer_Rates_in_US_Counties.pdf&rct=j&frm=1&q=&esrc=s&sa=U&ei=2vzoU8CoJKfgsAS1jIDwDQ&ved=0CBQQFjAA&usg=AFQjCNGhrf_08hFvxIIv3uNfmB1xIhfk6w