Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards. Heather wins the game if she draws a heart, and Blake wins the game if he draws a black card. When a player doesn't win on his or her turn, the card is returned to the deck, the deck is reshuffled, and it becomes the other player's turn. The game has four states: Heather Wins, Blake Wins, Heather's Turn, Blake's Turn.
(a) Draw the transition diagram for the Markov process.
(b) Set up an absorbing stochastic matrix for the Markov process.
(c) Find the stable matrix.
(d) What is the probability that Heather wins if she goes first?
(e) What is the expected number of turns if Heather goes first?