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#1 2014-02-12 15:41:05
- Dragonshade
- Member
- Registered: 2008-01-16
- Posts: 147
probability question (don't know if I did this right)
It is probably really simple, but I don't have an easy solution ( not even sure if I did it right)
so 8 people have their assigned seats, If we shuffle them around, what is the probably of all 8 not sitting on their assigned seats
Here is what I did
I solve this recursion with computer program, it gives
is about 37%Am I doing it right?
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#2 2014-02-12 16:01:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: probability question (don't know if I did this right)
Hi;
This is called a derangement problem. The formula for the number of derangements is
when we plug in n = 8 we get 14833.
Probability is defined as success / ( success + failure) so we have
For the full explanation see
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 2014-02-12 16:28:55
- Dragonshade
- Member
- Registered: 2008-01-16
- Posts: 147
Re: probability question (don't know if I did this right)
Oh cool! thanks, didn't know there was this type of problem. Looks like I got the right answer
The reason I got this problem is , one of my english teacher, she groups students in 8 and ask them to make one comment on other group member other than themselves. So in this way, only 37% chance everyone gets a comment which is a massive fail lol. I am going to email her about it : )
Last edited by Dragonshade (2014-02-12 16:37:52)
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#4 2014-02-12 16:29:57
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: probability question (don't know if I did this right)
Check it up against the known formula for a couple more.
Did you get all the right answers?
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 2014-02-12 16:39:39
- Dragonshade
- Member
- Registered: 2008-01-16
- Posts: 147
Re: probability question (don't know if I did this right)
my number is exactly the same as yours. So I think I got it right
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#6 2014-02-12 16:41:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: probability question (don't know if I did this right)
I checked yours out too. It seems correct and the reasoning good. Very good!
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 2014-02-12 16:59:28
- Dragonshade
- Member
- Registered: 2008-01-16
- Posts: 147
Re: probability question (don't know if I did this right)
thank you for the help : )
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#8 2014-02-12 17:05:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: probability question (don't know if I did this right)
Hi;
Glad to help.
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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