Question

If the animal is in the woods on one observation, then it is four times as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is twice as likely to be in the meadows as the woods on the next observation.
Assume that state 1 is being in the meadows and that state 2 is being in the woods.

If the animal is in the woods on the first observation, what is the probability that it is in the woods on fourth observation

Answer 1

My solution to the problem is as follows:

day 1: 1 
day 2: 0.6667 
day 3: 0.5111 
day 4: 0.4385 <-------

Therefore, the probability that the animal is in the woods on fourth observation would be 0.4385.

I hope my answer has come to your help. God bless and have a nice day ahead!