Re: How two probabilities are related

Thanks.

I would like to expand on my question.

This involves Bayesian theory, I think.

4 balls in an urn and there is replacement.
You don't know what the probability of red balls is.
You make an assumption that the priori distribution of red balls is
uniform, ie, that the probabilities that the urn contains 0, 1, 2, 3,
or 4 red balls are equal ie 1/5.

How do you obtain the posterior distribution of what the distribution
of the probabilities of being 0,1,2,3,or 4 red balls?

I've started with this using the previous posts response.

p[Red] = p[r=0]*0/4 + p[r=1]*1/4 + p[r=2]*2/4 + p[r=3]*3/4 + p[r=4]*4/4

the likelihood function is:
f(x1,x2,...,xn|r) = product_i=1_to_n (4 choose 1)*p[Red]*(1-p[Red])^3,
where p[Red] is as defined above

f(r) = 1, since it is a uniform distribution

Hence, f(x1,x2,...,xn,r) = f(x1,x2,...,xn|r).

I don't know how to get f(x1,x2,...,xn) since I don't know p[Red]
independent of p[r].

What I'm trying to do is plug this into:
f(r|x1,x2,...,xn) = f(x1,x2,...,xn,r)/f(x1,x2,...,xn)

.

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