- #1
Aleoa
- 128
- 5
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?
What is the correct Markov Matrix that represent this scenario ?
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?
What is the correct Markov Matrix that represent this scenario ?
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