A player bets on coin tosses, a dollar each time, and the game ends if the player has no money oris up to five dollars, and otherwise continues until exactly 20 bets have occurred. The playerwins when the coin lands heads side up, and loses when it lands tails side up. The coin is biased,landing heads side up only 48% of the time (instead of the usual 50%), and lands tails side up52% of the time.(a) Give the transition matrix M for the corresponding Markov chain.(b) (Using the online app at matrixcalc.org/en, clicking the "Display decimals" checkbox andsetting the number of fraction digits to 5.)If the player starts with two dollars, with what probability does the player have no money at theend of the game?

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(a) Give the transition matrix M for the corresponding Markov chain. (b) (Using the online app at matrixcale.org/en , clicking the "Display decimals" checkbox and setting the number of fraction digits to 5.) If the player starts with two dollars, with what probability does the player have no money at the end of the game?

(a) Give the transition matrix M for the corresponding Markov chain. (b) (Using the online app at matrixcale.org/en , clicking the "Display decimals" checkbox and setting the number of fraction digits to 5.) If the player starts with two dollars, with what probability does the player have no money at the end of the game?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Question

A player bets on coin tosses, a dollar each time, and the game ends if the player has no money or
is up to five dollars, and otherwise continues until exactly 20 bets have occurred. The player
wins when the coin lands heads side up, and loses when it lands tails side up. The coin is biased,
landing heads side up only 48% of the time (instead of the usual 50%), and lands tails side up
52% of the time.
(a) Give the transition matrix M for the corresponding Markov chain.
(b) (Using the online app at matrixcalc.org/en, clicking the "Display decimals" checkbox and
setting the number of fraction digits to 5.)
If the player starts with two dollars, with what probability does the player have no money at the
end of the game?

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