"99% of the time the concern is over a one in 100,000 event"
Not for this. Intense Solar Storm => can flip random bits for 1 to zero or vice versa.
This happens normally on flights flying at the altitude they are. So there are basic error correction codes in there already like Jolui said. A storm like this is a lot more than "normal", so they can add more checks. A common strategy is having three independent programs and if an error occurs in one the other two outvote it and lock it out. There are other techniques.
https://en.wikipedia.org/wiki/Single-event_upset
[snip]
On October 7, 2008, Qantas Flight 72 at 37,000 feet, one of the plane's three air data inertial reference units had a failure, causing incorrect data to be sent to the plane's flight control systems. This caused pitch-downs and caused severe injuries to crew and passengers. All potential causes were found to be "unlikely," or "very unlikely," except for an SEU, whose likelihood couldn't be estimated.[6]