Suppose we have a barrel with three different kinds of marbles: red, green and blue. The probability to find a red marble in the barrel is R0, analogously the probability for green is G0 and for blue is B0. We pour some of the marbles in a smaller bucket. Now the probabilities in the bucket are R1, G1 and B1. Finally, we pour from the bucket some marbles in a glass. The probabilities in the glass are R2, G2 and B2.
What are the expected values for R2, G2 and B2?
I can solve this problem if I know R0, G0, B0, G1 and B2, and consider the information about Xi (where X can be R, G or B) that I obtain from Xi+1 negligible.But what can I say if this information isn't negligible? Or if I only know R0, G1, B2?
Thanks a lot. I don't even know what can I read to solve the problem.