Question

(25) A game has two boxes as follows: Box A initially contains 2 white balls Box B initially contains 3 red balls. At each step in the game, 1 ball is selected at random from each box and the 2 balls are interchanged. Thus, Box A always contains 2 balls, and Box B always contains 3 balls. The game continues indefinitely. The game may be described by a Markov chain having three states: S0,S1,S2, whose subscript denotes the number of red balls in in Box A respectively. a). Make a table showing the contents of each box for the three states S0,S1,S2. b). Find the state transition probability matrix P. c). Draw a state transition diagram. d). Assuming the game starts in state So , find the probability that there are 2 red balls in Box A after 3 steps. e). Find the probability that there are 2 red balls in Box A in the long run.

Answer 1

Considen he alove given hat Cach box fon he thee states So, Si, S В ох в Box A ORed Rahite 3 Red So R Red lhite TRed hite SRed ouhite Red hite state tan sition frobbil S 2 So P

state tansikon diagrar the Potobbili het there 2ed blls in hox A attes 3 step s is 2s lett etgen ve chor cornel pondiny hoegen Velue is(o,0.6,0-3) So the Paokehil hat thene e ed balls in box A is o 3