A 24-hour, date-less, digital wrist-watch loses accuracy everyday, falling behind atomic time by an additional 15 minutes (every day). On the date of its manufacture, 1.1.2000 00h:00m:00s, it was perfectly synchronized to atomic time, and the malfunctioning applied every 24 hours thereafter.
A customer buys the watch on 1.1.2017 00h:00m:00s and assumes, rather stupidly, that the time displayed is accurate. After purchase, when mentioning the time to any one who asked, what is the probability that the time our buyer mentions is within +/- 1 minute of atomic time?
(Assume everlasting battery, consider leap years if needed, post purchase the watch still malfunctions everyday as usual, watch displays ONLY hh:mm, and not seconds).
- Beginning probability student here, solving some harder problems (from the competitive math space)
- Not looking for a number answer or an outright solution, but hints, possible approaches.