Broken clock/watch odds
February 7th, 2023 at 10:03:55 AM
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What are the percentage odds of looking at a broken/non-running watch or clock at any random time of day, and having it be exactly on time?
I.e., you look at the current time on your phone and it is 10:37. You then look at a broken clock and at some point in the past it has stopped at 10:37.
Assume:
Analog dial.
AM/PM is irrelevant.
Accuracy is up to two minutes in either direction. So in the above example, the clock could be stopped anywhere between 10:35 and 10:39 and that would count as "exactly on time."
Context: I feel like this happens to me a lot and I'm curious as to what the odds of it are.
I.e., you look at the current time on your phone and it is 10:37. You then look at a broken clock and at some point in the past it has stopped at 10:37.
Assume:
Analog dial.
AM/PM is irrelevant.
Accuracy is up to two minutes in either direction. So in the above example, the clock could be stopped anywhere between 10:35 and 10:39 and that would count as "exactly on time."
Context: I feel like this happens to me a lot and I'm curious as to what the odds of it are.
February 7th, 2023 at 10:07:01 AM
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1/144
February 7th, 2023 at 10:15:07 AM
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Quote: SOOPOO
This. So if you look at 100 broken clocks there is just over a 50% chance that at least one of them is showing the right time.
(143/144)^X = 50%
X = ln(0.5)/ln(143/144) = 99.46621279
Also reminds me of one of my favorite expressions when someone comes up with the right answer:
Even a broken clock is right twice a day.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 7th, 2023 at 11:42:42 AM
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More than once have I looked at one of my wall clocks in which the battery has died, and the time was close enough to the actual time that I thought the clock was working.
February 7th, 2023 at 12:02:33 PM
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I've frequently glanced at a wall clock whose battery had died and assumed it was still in operation since the time was near enough to the real time
February 7th, 2023 at 12:02:43 PM
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Might as well just use broken clocks
It’s all about making that GTA
February 7th, 2023 at 12:21:52 PM
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1/720
"Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things."
-- Isaac Newton
February 7th, 2023 at 12:37:26 PM
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Not sure how you came up with that.Quote: SOOPOO
A broken clock is correct twice each day.
60 * 24 / 2 = 720
So it’s 1/720
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
February 7th, 2023 at 12:50:50 PM
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Quote: DJTeddyBearNot sure how you came up with that.Quote: SOOPOO
A broken clock is correct twice each day.
60 * 24 / 2 = 720
So it’s 1/720
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720 minutes. OP said it’s close enough if the clock is plus or minus 2 minutes. So that’s a 5 min window. 720/5 = 144
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
February 7th, 2023 at 1:17:09 PM
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Quote: DJTeddyBearNot sure how you came up with that.Quote: SOOPOO
A broken clock is correct twice each day.
60 * 24 / 2 = 720
So it’s 1/720
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The OP gave a minute or two on each side of the correct time, so wouldn't it be 5/720 or 144?
The older I get, the better I recall things that never happened
February 7th, 2023 at 1:26:10 PM
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4/(12*60) = 1/180.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 7th, 2023 at 2:03:13 PM
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Quote: Wizard
4/(12*60) = 1/180.
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I can’t believe this is wasting so many electrons. There are 5 minutes where the clock will be ‘correct’ as per the OP’s definition. The correct time plus two on either side. So that’s 5 of the 720 minutes that are possible in a 12 hour cycle. 5/720 is 1/144.
Like I said one minute after starting to think about this….
February 8th, 2023 at 1:54:19 AM
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Quote: SOOPOOLike I said one minute after starting to think about this….
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I am going by time down to the second.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
