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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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#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.

 

 

Can someone please help and explain the correct answer if it exist at all.

 

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!


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#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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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#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

Any moderator reading this, please help me out, i am trying to Mark Solved multiple answers but now i cannot mark any of the answers as solved.


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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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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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