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Guest
Guest
I've been trying to do this problem for some time now, and am very confused.
Here it is:
You are at a charity gambling event and are playing a simple game. You spin a wheel with the numbers 1 to 10 on it (each number is equally likely to come up.) If you get a 1 to 4, you win $1, 5 to 10 you lose $1. Suppose you have $2 to play with. You decide to stop playing if you run out of money or if you have $4.
1. Set up a transition matrix for this problem. (hint: the states represent how much money you have; there should be five states.)
2. What is the probability that you will have $4 after the first two rounds? Explain, without using matrices, why this answer makes sense.
3. Find the probability that you have lost all your money within 8 rounds.
4. What will happen in the "Long Run?" Explain your answer. (Matrix A times Matrix B to the 100th power.)
5. What happens to the probablity of ending up with $4 if you start with $1 or $3? Explain your answer.
I'm confused. I don't know how to set up the matrix, so any help would be appreciated. Thanks in advance.
Here it is:
You are at a charity gambling event and are playing a simple game. You spin a wheel with the numbers 1 to 10 on it (each number is equally likely to come up.) If you get a 1 to 4, you win $1, 5 to 10 you lose $1. Suppose you have $2 to play with. You decide to stop playing if you run out of money or if you have $4.
1. Set up a transition matrix for this problem. (hint: the states represent how much money you have; there should be five states.)
2. What is the probability that you will have $4 after the first two rounds? Explain, without using matrices, why this answer makes sense.
3. Find the probability that you have lost all your money within 8 rounds.
4. What will happen in the "Long Run?" Explain your answer. (Matrix A times Matrix B to the 100th power.)
5. What happens to the probablity of ending up with $4 if you start with $1 or $3? Explain your answer.
I'm confused. I don't know how to set up the matrix, so any help would be appreciated. Thanks in advance.
