There are some balls with 4 different colors in a black box. The ratio of A color ball is 10%, B is 20%, C is 30% and D is 40%.
The rule of this game is that you randomly pick one ball and mark the color of this ball then throw it back to the box.
The Question is: When you already have marked 2 different color balls, what is the probability of that the next time you pick one ball is the same color with the previous 2 colors (P22), and is different with previous 2 colors (P23).
Here is what I thought: Use Markov matrix to solve the problem, the states are AB AC AD BC BD CD ABC ABD BCD ACD, so we can build a $10 * 10$ matrix T: $$AB->AB = 0.3, AB->AC=0.0 ... AB->ABC=0.3, AB->ABD=0.4$$ etc.
calc: $$\lim_{n\to\infty} {T}^n$$ I am not sure this method is correct.
Is this a Poisson Process?