A bucket contains four red and three green balls. The probability of picking a ball is equal. If a red ball is chosen, it is removed from the bucket and if a green ball is picked, it is placed back into the bucket. The game continues until all four red balls are removed from the bucket.
Model this game as a Markov chain and calculate the expected number of steps before the game finishes.
Now, I'm not quite sure how to draw a probability tree diagram using Latex, so I won't do so, but I can certainly model it like this but I am a bit confused when it comes to setting this up as a Markov chain.
My initial thoughts is that I will have two separate ones, depending on what colour ball I first pick. Is that the way to go about it? If so, I will edit this and show my attempt at it. If there indeed is a way to collate this as one Markov chain, then I would very much appreciate a pointer as to where to begin.
Thanks in advance.
Each state will be the number of red balls remaining. The probabilities in the transition matrix will correspond to the probability that a ball chosen at random from what remains is red.