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**Mentor note: Thread moved from Mathematics section, so is missing the HW template**

John and Eli are playing a game with a hall that can roll into one of two

pockets labelled H and Y. John wants to keep the hall in H and Eli wants

to keep it in Y. When it is John's turn to play, ifhe finds the hall in H that is

fine with him and he does nothing; but if he finds it il). Y he attempts to roll

it into pocket H. This takes some skill; the probability that he succeeds is 2/3 ,

there being a 1/3 chance that the hall will roll back into Y. When Eli's turn

comes, he does nothing if the hall is in Y, but tries to get it there ifhe finds it

in H. Eli is less skillful than John and his probability of succeeding in bis

effort is only 1/2.

I built this 2x2 matrix:

[tex]

A=\begin{bmatrix}

\frac{1}{3} & \frac{1}{2}\\

\frac{2}{3} & \frac{1}{2}

\end{bmatrix}[/tex]

The first colum is for state Y and the second for the state H.

But, when i read the first exercise to do with this matrix, it seems not properly built:

**(a)Starting with the hall in Y and John to play, what is the probability**

that the hall will be in H after John's second play?

that the hall will be in H after John's second play?

What is the correct Markov Matrix that represent this scenario ?

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