Inaccurate 5-Minute Timer

....

What?

• "Exact" atomic time is ubiquitous. Maybe people were happier back when they didn't have perfect seconds and looked at the sun and water clocks for accuracy. Since correlation = causation and there are no coincidences, I'm sure the secret to happiness is not being bound by perfect time (unless you're being taken care of by doctors or are working in a nuclear facility).
• Each second of this 5-minute timer is randomly offset. There's a chance that it will be accurate during its entire run, which is astronomically small and which I'll calculate later (or that you can calculate yourself if you want). I'd assume each offset independent and uniformly distributed between -1000 and 1000 milliseconds.