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| robjay... |
 Posted: Mon Oct 26, 2009 3:37 am |
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Guest
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Hi
I am having problems generalising the following problem.
Say you have five (1,2,3,4,5) people which are selecting colours that
they like from the possible choices of Red, Green or Blue. They may
select more than one colour, but they must select at least one colour.
It's easy to answer questions like, Given a person has selected two
colours, what is the probability that they have Red in their selection
(2/3).
If we are then given extra information, then it can make it much
harder to answer this same question. If for example we are told that 4
people liked Red, 4 People liked Green, but only one person liked
Green, then answering the above question becomes much harder.
By considering the possible combinations I have managed to calculate
that given a person who says they like two colours, the probability
that they like Red is 14/15, Blue is 14/15 and Green is 2/15.
My problem is that I can't figure out how to derive a general result,
when there are C colours, n people, and some given numbers for the
number of people who liked a particular colour.
Any help that anyone may be able to give me would be gratefully
received.
Cheers
James |
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| root... |
| Posted: Mon Oct 26, 2009 8:20 am |
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robjay <james.robertson75 at (no spam) yahoo.co.uk> wrote:
[quote]
If we are then given extra information, then it can make it much
harder to answer this same question. If for example we are told that 4
people liked Red, 4 People liked Green, but only one person liked
Green, then answering the above question becomes much harder.
[/quote]
Your statement of the problem is confusing to me, as illustrated
by the paragraph above. Did you mean that only one person liked
green only?
Sort the data first by number of colors selected. Then you
can answer your questions within the separate groups. That
is, within the group of people who selected n colors, a
fraction x selected red as one of those colors. You can
also say things like "a fraction y of the people selected
n colors". |
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| robjay... |
| Posted: Mon Oct 26, 2009 8:40 am |
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Guest
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On 26 Oct, 18:20, root <NoEM... at (no spam) home.org> wrote:
[quote]robjay <james.robertso... at (no spam) yahoo.co.uk> wrote:
If we are then given extra information, then it can make it much
harder to answer this same question. If for example we are told that 4
people liked Red, 4 People liked Green, but only one person liked
Green, then answering the above question becomes much harder.
Your statement of the problem is confusing to me, as illustrated
by the paragraph above. Did you mean that only one person liked
green only?
Sort the data first by number of colors selected. Then you
can answer your questions within the separate groups. That
is, within the group of people who selected n colors, a
fraction x selected red as one of those colors. You can
also say things like "a fraction y of the people selected
n colors".
[/quote]
Really sorry, there is a mistake in in my original post, it should
read
4 people liked Red, 4 People liked Blue, but only one person liked
Green.
That is, 4 out of the 5 people said they liked Red, 4 out of the five
people said they liked Blue (But not necessarily the same 4 who said
they liked Red) and 1 out of the 5 people said they liked Green.
My problem is how do you calculate the probabilities if you DON'T have
the data to form the groups, that is, if you don't know the individual
distribution of liked colours for people who liked n colours.
Thanks
James |
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| root... |
| Posted: Mon Oct 26, 2009 9:43 am |
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Guest
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robjay <james.robertson75 at (no spam) yahoo.co.uk> wrote:
[quote]
My problem is how do you calculate the probabilities if you DON'T have
the data to form the groups, that is, if you don't know the individual
distribution of liked colours for people who liked n colours.
Thanks
James
[/quote]
I'm sorry, but once again I don't understand what you need. Are
you saying you don't have any preference data? Do you only know
how many colors each person chose? |
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| robjay... |
| Posted: Mon Oct 26, 2009 10:49 am |
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Guest
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[quote]I'm sorry, but once again I don't understand what you need. Are
you saying you don't have any preference data? Do you only know
how many colors each person chose?
[/quote]
Ok, say you have the following data, and only the following data:
5 people, for each of whom you know how many colours they said they
liked (some number between 1 and 3 inclusive).
3 colours, for each of which you know how many people said they liked
that colour.
The question is, given that a person says they like two colours, what
is the probability that Red is one of those two colours?
Hope this makes more sense to you.
James |
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| root... |
| Posted: Mon Oct 26, 2009 8:00 pm |
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Guest
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robjay <james.robertson75 at (no spam) yahoo.co.uk> wrote:
[quote]I'm sorry, but once again I don't understand what you need. Are
you saying you don't have any preference data? Do you only know
how many colors each person chose?
Ok, say you have the following data, and only the following data:
5 people, for each of whom you know how many colours they said they
liked (some number between 1 and 3 inclusive).
3 colours, for each of which you know how many people said they liked
that colour.
The question is, given that a person says they like two colours, what
is the probability that Red is one of those two colours?
Hope this makes more sense to you.
James
[/quote]
In your example you have 8 numbers. In general you have N+C numbers.
Except in the most trivial of cases I would agree with Mr. Koopmans
that you can't do too much. This isn't really a statistics question. |
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| robjay... |
| Posted: Tue Oct 27, 2009 2:56 am |
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Guest
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[quote]This isn't really a statistics question.
[/quote]
I really do not understand what you mean by this. I can't see what
sort of problem this is, other than one which is statistical in
nature. Unless you mean that it is a combinatorial problem, which I
thought was the bread an butter of statistics. |
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