Suppose we have a board with four squares marked 1, 2, 3, 4 as in the picture: 3 We play a game where a counter is placed on one of the squares and we move it to an adjacent square with probability given by the following table: Current position can move to these positions with this probability 2 with probability 4, 3 with probability I with probability , 4 with probability I with probability 4, 4 with probability 2 with probability , 3 with probability 2 3 Let x be a vector such that r, is the probability that the counter is on square i. (a) Write down a stochastic matrix A such that vector Ax gives the probability for the position of the counter after one move. (b) Suppose we begin the game by placing the counter on square num- ber 1. Use your matrix from part (a) to calculate the probability it is on square I after two moves.
Suppose we have a board with four squares marked 1, 2, 3, 4 as in the picture: 3 We play a game where a counter is placed on one of the squares and we move it to an adjacent square with probability given by the following table: Current position can move to these positions with this probability 2 with probability 4, 3 with probability I with probability , 4 with probability I with probability 4, 4 with probability 2 with probability , 3 with probability 2 3 Let x be a vector such that r, is the probability that the counter is on square i. (a) Write down a stochastic matrix A such that vector Ax gives the probability for the position of the counter after one move. (b) Suppose we begin the game by placing the counter on square num- ber 1. Use your matrix from part (a) to calculate the probability it is on square I after two moves.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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Transcribed Image Text:Suppose we have a board with four squares marked 1, 2, 3, 4 as in the
picture:
3
We play a game where a counter is placed on one of the squares and we
move it to an adjacent square with probability given by the following
table:
Current position can move to these positions with this probability
2 with probability 4, 3 with probability
I with probability , 4 with probability
I with probability 4, 4 with probability
2 with probability , 3 with probability
2
3
4
Let x
be a vector such that r, is the probability that the
counter is on square i.
(a) Write down a stochastic matrix A such that vector Ax gives the
probability for the position of the counter after one move.
(b) Suppose we begin the game by placing the counter on square num-
ber 1. Use your matrix from part (a) to calculate the probability
it is on square I after two moves.
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