An urn contains six tags, of which three are red and three green. Two tags are selected from the urn. If one tag is red and the other is green, then the selected tags are discarded and two blue tags are returned to the urn.
Otherwise, the selected tags are returned to the urn. This process repeats until the urn contains only blue tags. Let X,, denote the number of red tags in the urn after the nth draw, with Xo = 3.
(This is an elementary model of a chemical reaction in which red and green atoms combine to form a blue molecule.) Give the transition probability matrix.