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#1 2016-08-21 02:56:07
- FRATQU33N
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- Registered: 2016-08-21
- Posts: 14
Intro Probability UNI LEVEL
Hey Guys, Having trouble understanding how to work out this question, any help or intuition would be much appreciated.
Thank you 
Last edited by FRATQU33N (2016-08-22 01:25:12)
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#2 2016-08-21 02:57:51
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Intro Probability UNI LEVEL
Hi;
This is a derangement problem. have you covered that?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2016-08-21 03:00:16
- FRATQU33N
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Re: Intro Probability UNI LEVEL
No I have not 
What is it ?
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#4 2016-08-21 03:02:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Intro Probability UNI LEVEL
In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2016-08-21 03:04:11
- FRATQU33N
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- Registered: 2016-08-21
- Posts: 14
Re: Intro Probability UNI LEVEL
Thank you! How could i employ this in this scenario?
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#6 2016-08-21 03:16:19
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Intro Probability UNI LEVEL
I will work on it.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2016-08-21 03:22:10
- FRATQU33N
- Member
- Registered: 2016-08-21
- Posts: 14
Re: Intro Probability UNI LEVEL
Thank you for your time!
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#8 2016-08-21 05:51:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Intro Probability UNI LEVEL
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2016-08-21 16:34:43
- thickhead
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- Registered: 2016-04-16
- Posts: 1,086
Re: Intro Probability UNI LEVEL
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#10 2016-08-21 16:49:26
- thickhead
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- Registered: 2016-04-16
- Posts: 1,086
Re: Intro Probability UNI LEVEL
My answer is definitely wrong. It refers to a case when the remaining 3 get neither correct hat nor coat. It is different from what is asked.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#11 2016-08-21 17:00:46
- FRATQU33N
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- Registered: 2016-08-21
- Posts: 14
Re: Intro Probability UNI LEVEL
My answer is definitely wrong. It refers to a case when the remaining 3 get neither correct hat nor coat. It is different from what is asked.
Thats okay thank you for your time
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#12 2016-08-21 17:01:52
- FRATQU33N
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Re: Intro Probability UNI LEVEL
Hi;
Awesome! What method was employed. Im having twouble connecting P(Exactly 2 have correct hats) and P(Same two have correct coat)
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#13 2016-08-21 17:07:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Intro Probability UNI LEVEL
These double derangement or ( hat and coat ) problems are always a big pain in neck. The only analytical approach I know of is PIE and I do not use it.
Luckily these problems are rather well known so there is a formula and of course there is a direct computer count.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2016-08-21 17:20:59
- FRATQU33N
- Member
- Registered: 2016-08-21
- Posts: 14
Re: Intro Probability UNI LEVEL
WHat is PIE?
ah
inclusion exclusion?
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#15 2016-08-21 17:23:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Intro Probability UNI LEVEL
Yep, Principle of Inclusion Exclusion, PIE for short.
Welcome to the forum.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2016-08-21 18:34:43
- thickhead
- Member
- Registered: 2016-04-16
- Posts: 1,086
Re: Intro Probability UNI LEVEL
I endorse bobbym's answer as correct. For a student when logic fails one has to go for sample space.
There are 26 ways in which 3 persons do not get their coats properly or hats properly.So the probability boils down to
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#17 2016-08-22 00:22:46
- thickhead
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- Registered: 2016-04-16
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Re: Intro Probability UNI LEVEL
Hi FRATQU33N,
I have cooked a logical method.See whether it is tasty.
2 persons can be selected in
Now concerning remaining 3 persons. They can collect their coats in 3! different ways and so with their hats. the total number of ways is 36. Let us call them A,B and C.
Out of 36 ways A can select his coat in 36/3 ways and further correct hat in 36/3/3=4 different ways.
But A ,B and C all get their correct coat and hat in only 1 way.
So the the number of ways in which one collects his things correctly but not others is 4-1=3ways.
So the number of ways in which at least one collects his things is=3*3+1=10 ways.
The number of ways in which none collects his own things=36-10=26
The total number of ways in which coats and hats can be collected=5!*5! ways.
So the probability required=
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#18 2016-08-22 02:04:48
- thickhead
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- Registered: 2016-04-16
- Posts: 1,086
Re: Intro Probability UNI LEVEL
You may also note that A and B collecting correct things and C not collecting is impossible and therefore not included.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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