complicated selection problem
robjay
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
robjay
> 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.
Sorry, but there is an error in the above. It should read
4 people liked Red, 4 People liked Blue, but only one person liked
Green.