Thread: Markov chain

Suppose three out of every four trucks on the road are followed by a car, while only one out of every five cars is followed by a truck. What fraction of vehicles on the road are trucks?

I form a markov chain as followed:



Then find the limiting probabilities and I got 0.2105.

Am I right?

Yup, thats what i got, since its irreducible finite markov chain there is a stationary distribution, which is the proportion of time the chain spends in each state;
If 0 is the event of a truck, 1 is a car (as outlined in your transition matrix) then


And

So solving,