Concept explainers
(a)
To graph: The transition diagram for Markov process, if 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 hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.
(b)
To calculate: The absorbing stochastic matrix for the Markov process, if 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 hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.
(c)
To calculate: The stable matrix, if 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 hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.
(d)
To calculate: The probability that Heather wins if she got first, if 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 hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.
(e)
To calculate: The expected number of turns if heather got first, if 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 hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.
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