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#1 2013-08-08 02:24:41

anna_gg
Member
Registered: 2012-01-10
Posts: 105

Shoelace

A shoelace is lying on the floor, and attached you can see its shadow. If I pull it, what is the probability that it will produce a knot?

View Image: knot.jpg

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#2 2013-08-08 03:03:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,813

Re: Shoelace

Hi anna_gg


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2013-08-08 03:18:25

anna_gg
Member
Registered: 2012-01-10
Posts: 105

Re: Shoelace

All I can tell is that there are 7 intersections, so there are 2^7 =128 possible ways the shoelace can cross itself. Of these, we should keep only the ones that are "over/under/over" and "under/over/under", which will produce a knot. But I cannot figure out how many these are.

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#4 2013-08-08 03:30:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,813

Re: Shoelace

Um, have you seen my answer?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2013-08-08 03:46:38

anna_gg
Member
Registered: 2012-01-10
Posts: 105

Re: Shoelace

anonimnystefy wrote:

Um, have you seen my answer?

Yes, but I do not understand how you calculate it smile

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#6 2013-08-08 06:29:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,813

Re: Shoelace

Well, I looked at the two parts separately, because they are virtually independent. For one, there are 8 possibilities for one and 16 for the other. Then I just combine them.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2013-08-09 05:47:55

anna_gg
Member
Registered: 2012-01-10
Posts: 105

Re: Shoelace

anonimnystefy wrote:

Well, I looked at the two parts separately, because they are virtually independent. For one, there are 8 possibilities for one and 16 for the other. Then I just combine them.

So you mean that in the right part there are only 3/16 possibilities that a knot is produced? Because at the left part I see there are 2/8, that is 4/16.

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#8 2013-08-09 05:51:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,813

Re: Shoelace

No, both probabilities are 1/4.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#9 2013-08-09 06:48:28

anna_gg
Member
Registered: 2012-01-10
Posts: 105

Re: Shoelace

anonimnystefy wrote:

No, both probabilities are 1/4.

So, how do you get 7/16? Am confused smile

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#10 2013-08-12 04:51:14

anna_gg
Member
Registered: 2012-01-10
Posts: 105

Re: Shoelace

Got it. You don't add the two sections, you multiply them smile

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#11 2013-08-12 04:55:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,469

Re: Shoelace

How did you get 7 / 16 by multiplying?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2013-08-12 19:28:11

anna_gg
Member
Registered: 2012-01-10
Posts: 105

Re: Shoelace

bobbym wrote:

How did you get 7 / 16 by multiplying?

The probability for both parts NOT to produce a knot is 3/4 for each (since the probability to produce a knot is 1/4). Therefore the total probability NOT to have a knot is 3/4*3/4 = 9/16, thus giving us probability to have a knot 1-9/16 = 7/16.

It wasn't me who solved it, I just unraveled anonimnystefy's solution smile

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#13 2013-08-12 20:09:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,469

Re: Shoelace

Hi;

Okay, thanks for the answer.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#14 2013-08-18 01:32:09

bohr
Member
Registered: 2013-08-18
Posts: 1

Re: Shoelace

I understand that the left part has a probability of 1/4 to produce a knot, since only two of the eight possible ways produce a knot (over/under/over and under/over/under). However, how the right part has also 1/4 probability; You mean that from the 16 possible ways, 4 of them produce a knot;

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