Probability of Hunting in B on Thursday Given C on Monday

[subopolois]

Homework Statement

some may have seen my other post on markov chains, this is just an extention, something i forgot to ask. the second part of the question asks: If he hunts in C on Monday, what is the probability that he will hunt in B on Thursday?

Homework Equations

markov chain theroms: Ssub0 and PSsub0= Ssub1

The Attempt at a Solution

now the question asks if he hunts on c on monday, my question only relates to this part, i know how to do the rest. so if he hunts in c on monday which is Ssub0, my question is since i know he hunts in c on monday, is Ssub0 {0 0 1}? likewise if he hunted in b mon monday it would be {0 1 0}?

 

[mighty2000]

I would approach this problem by first understanding the basics of Markov chains and their properties. I would then carefully read the question and identify the important variables and information provided. In this case, the variables are the different hunting locations (A, B, C) and the days of the week (Monday, Thursday). The information provided is that the person hunts in C on Monday.

Next, I would use the Markov chain theorem to determine the probabilities for each possible outcome. In this case, there are three possible outcomes: hunting in A, B, or C on Thursday. The probabilities for each outcome can be calculated using the transition matrix and the initial state probabilities.

To answer the question, I would use the information provided (hunting in C on Monday) to update the initial state probabilities and then use the transition matrix to calculate the probability of hunting in B on Thursday. This can be done by multiplying the initial state probabilities by the transition matrix and then looking at the corresponding value for B on Thursday.

In summary, as a scientist, I would approach this problem by understanding the fundamentals of Markov chains and using the given information to calculate the desired probability. I would also double-check my calculations and make sure they align with the properties of Markov chains.