# What are the odds of seeing any one number sequence on a clock during a 16 hr period?

I need this information for a SE cognitive sciences question, which I've not yet posted, so I can't link to it yet. It has to do with the probability of seeing the same number on a clock seemingly disproportionately to other times. For instance, one may see 1:23 or 11:11 or 1:11 or 3:14 or 4:20, whatever, and think they see it more often than other number sequences. Assume normal time, not military (24hr) time. And digital, not analog.

I was figuring, during a 12 hr period, the odds would be 1 out of 720 (1 x 9 x 6 x 10 + 1 x 3 x 6 x 10) for seeing any one sequence. A 24hr period would be 1 out of 360, right? So what would the odds be for a 16 hr period? 1 out of 600??? (720 - (1 x 4 x 6 x 10)/2).

People generally sleep 8 of the 24hrs, leaving 16hrs to look at the clock. If someone sleeps from midnight to 8am, what are the odds of noticing the clock displaying 11:11 if they check the clock N times a day? How about 1:11?

It seems like I'm missing something. If someone checks the clock N times a day, do they check it more at the beginning or end of the day? Is it evenly distributed? Would it follow some other distribution curve? If so, how does that factor into the odds? I don't need necessarily a precise answer, I just want to say what the odds should fairly be for noticing any one number sequence on the clock and to decide if noticing a specifc sequence (11:11) 5 days in a row would be considered strange. Make any assumptions you think are reasonable to help me out with this one.

I've seen claims of N being 8 times and all the way up to 150 times a day.

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