There are three balls in the bag, Blue(B), Green(G), Red (R). Every balls were picked by equal probability and when it was picked, returns it to the bag on the right of the other two balls. Let X_n denote the ordering of the balls on time n. The steady-state probabilities for this chain are (0.167, 0.167, 0.167, 0.167, 0.167, 0.167).

1. If there are a balls, where a is from 1 to a, and picked by equal probability. Analyse the long-term behavior of this chain.

 2. There are still three balls in the bag, Blue(B), Green(G), Red (R). But the balls are picked by a random probability p, where p(n) > 0, n = 1, 2, 3. Analyse the long-term behaviour of this chain.