Probability problem

I wonder if someone can help me with this (it's not work or homework):

You have 2 different sized samples of metal ( A and B).

There are 3 types of metal (I, II, III).

You know beforehand that each type of metal is equally likely in the
"general population".

However you do some calculations:

These tell you that:
the probability of sample A being type I = 0.6; type II =0.3, type III
=0.1
and
the probability of sample B being type I = 0.3; type II = 0.5, type
III=0.2.

Later you discover that both samples are the same type of metal (but
you don't know which):

Can this new info now change these probabilities? If so, how?

.

Relevant Pages

  • Re: Advanced Monty Hall Problem with N door and M cars
    ... I promise you that this is not a homework. ... >> Assuming that we have N door with M of these door have cars behind ... >> What is the probability of winning if she stay with her choice? ...
    (sci.stat.math)
  • Re: permutation mappings
    ... > I agree the expectation value of the number of matches must be 1. ... > probability of the the first card she exchanges staying in place is ... Just keep thinking homework is fun, ...
    (sci.crypt)
  • Re: I have a statistics question
    ... If there are no calls in 10 minutes, what is the probability that the ... this looks like homework. ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.math)
  • Re: RSA algorithm
    ... > that using algorithm A we can invert every input with high ... > probability. ... Are you doing lakis's homework? ... --Mike Amling ...
    (sci.crypt)