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# Probability of a rope cut exactly in half, in a single slice

Best Answer kingofpain, 09 June 2013 - 06:37 PM

The probability that the cut us exactly in the middle is precisely 0. However, if you impose a tolerance, then you will receive a finite answer.

e.g. Rope is 10m long. The equality is defined as length of left side is equal to right side within 1 mm. This means that cutting anywhere from 4999.5mm to 5000.5mm will be ok. Therefore, the probability will be 1 in 10,000 if the probability of the cut at any point on the rope is equal.

Cheers!

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8 replies to this topic

### #1 Orochi663

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Posted 09 June 2013 - 02:27 PM

Hi,

I once read over the internet a question like:

You have a knife which is very sharp and a rope of unifoirm length, with a single cut what is the probability that the rope is cut exactly from half.

The who gave the answer 1/3 had the logic that there are only three possibilities of this experiment after the cut.

1. Left peice is bigger

2. right peice is bigger

3. left peice = right peice

so the probability he calculated is 1/3.

When i discussed with some of my friends they were not convinced on this answer, arguing that this type of experiment can have infinite possibilities.

Regards

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### #2 kingofpain

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Posted 09 June 2013 - 06:37 PM   Best Answer

The probability that the cut us exactly in the middle is precisely 0. However, if you impose a tolerance, then you will receive a finite answer.

e.g. Rope is 10m long. The equality is defined as length of left side is equal to right side within 1 mm. This means that cutting anywhere from 4999.5mm to 5000.5mm will be ok. Therefore, the probability will be 1 in 10,000 if the probability of the cut at any point on the rope is equal.

Cheers!

• 1

### #3 Anza Power

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Posted 09 June 2013 - 07:13 PM

The who gave the answer 1/3 had the logic that there are only three possibilities of this experiment after the cut.

1. Left peice is bigger

2. right peice is bigger

3. left peice = right peice

so the probability he calculated is 1/3.

Ok, so by that logic if I go and fill out the lottery, there are 2 possibilities, either I win or I lose,  so probability of me winning is 1/2...

But yeah as kingofpain said, the probability is 0, you can think of it like this: the rope is 1 meter long and you pick a number between 0 and 1 and slice there, now, how many numbers are there between 0 and 1?

(even if you think of the rope in a 3D space and give it a diameter the answer doesn't change)

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### #4 dark_magician_92

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Posted 10 June 2013 - 03:55 PM

i agree to the anza and kop. Tha answer can't be 1/3 because the concept is that if you divide the case in 3 possibilities and all cases have equal possibilities, only then one of the case has the prob = r/y. Hence in this case prob. Of cutting in middle is not as same as cutting less than or more than half, so 1/3 doesnt work.
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### #5 witzar

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Posted 10 June 2013 - 04:37 PM

there are only three possibilities of this experiment after the cut.

1. Left peice is bigger
2. right peice is bigger
3. left peice = right peice

so the probability he calculated is 1/3

It would be true, if all three possibilities were equally probable.

Which is not the case.

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### #6 bonanova

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Posted 11 June 2013 - 05:09 AM

It's the probability of picking the number 0.500... from all the real numbers in [0, 1].
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Vidi vici veni.

### #7 Orochi663

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Posted 14 June 2013 - 07:10 PM

Thanks guys...Analogoy by Bonanva really helped understanding the answer of king of pain.

Best Regards to All.

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### #8 Orochi663

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Posted 14 June 2013 - 07:15 PM

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### #9 bonanova

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Posted 17 June 2013 - 06:05 PM

Try again. It seems to work now. Or tell me the post number and I'll do it.
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Vidi vici veni.

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