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Double Digits

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.


Puzzle ID:#1112
Fun:*** (2.49)
Difficulty:*** (2.26)
Submitted By:starman****
Corrected By:shenqiang




As an inveterate clock watcher, James glances at his digital watch at random from time to time throughout the day. What is the probability that he will see all the digits reading the same (for example, 4:44) during any single glance? (Assume a typical day, not a day on which daylight savings time changes or anything like that. The watch is set to a 12 hour U.S. format, not a 24 hour European or military format.)

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Oct 17, 2001

Find me a watch that shows 00 instead of 120. It happens 12 times, not 14. It's .0083, not .0097.
Nov 16, 2001

If you are considering sleeping time then also probability will not change.If favourably chances are reduced then dividing factor will also get reduced.
Dec 05, 2001

I AGREE wit pizzahead! i too wanna see the watch that gives you the tyme 00?
(user deleted)
Feb 10, 2002

Agreeing with the 12 occurances, I must disagree with the calculation of probability for Jim, unless this inveterate "watcher" looks at the time "randomly" once during every minute cycle, in which case I might label him as OCD (obsessive-compulsive disorder). Anyway, there is a 12 in 1440 chance, approx. 0.83% (obviously) of the time occurances, but Jim's probability can only be based on the number of actual times he looks at his watch during the day, so if he looks at the reading 30 times per day, there would be a 25% chance (0.83*30)of him seeing identical digits.
Apr 04, 2002

You said that the time is American time, there IS no "00" in standard time, therefore the correct answer, assuming the person does not sleep is 1/120.
Apr 05, 2002

I assumed James had insomnia, but I forgot the 11:11 time. Good one, well done!
May 17, 2002

lamentor, read the question again. It clearly stated "what are the chances...DURING A SINGLE GLANCE". That's it. Also, I agree that there is no 00 on a digital watch.
Sep 29, 2010

Good problem. It taught me to just find number of minutes in 12 hours to get total # of possible times instead of count them w/ multiplication.
Mar 04, 2016

Don't know if anyone is still reading this. How's about taking this teaser one step further. What is the probability of looking at your watch and having the minutes and seconds match. and if one had the ability to see matches more frequently than predictable, what would that indicate.?

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