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


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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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  • Solution

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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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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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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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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The answer is not zero, but you would need more information, like cross sectional area, length,  weight or density of material, and molar mass of material. Relativisticly speaking it is infinitesimally close to zero, but definitely not zero, because we can predict the number of atoms or molecules, which is a lot... there is one factor that is 50/50 and that is whether there is an odd number or even number of atoms/molecules. imagine it like this, you are the size of an atom , you see a rope of 3 similar atoms bonded the probability becomes zero, just like if you had one atom...unless your knife is capable of splitting atoms the probability is 0... 2 atoms bonded your probabibility went up to one. 4 atoms and your probability is 3:7, as the number of atoms goes higher the probability drops.

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