# Math Help - Markov Chain Limiting Probabilities (Just need answer checked please)

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?

Let

state 0 represent seeing a truck
state 1 represent seeing a car

Then we have a probability matrix of

$\pi_{0}=0.25\pi_{0}+0.2(1-\pi_{0})$

$0.95\pi_{0}=0.2 =>\pi_{0}=\frac{2}{95}$

I just wanna make sure this is correct, and if not, what I'm doing wrong. Thanks

2. ## Re: Markov Chain Limiting Probabilities (Just need answer checked please)

Originally Posted by downthesun01
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?

Let

state 0 represent seeing a truck
state 1 represent seeing a car

Then we have a probability matrix of

$\pi_{0}=0.25\pi_{0}+0.2(1-\pi_{0})$

$0.95\pi_{0}=0.2 =>\pi_{0}=\frac{2}{95}$

I just wanna make sure this is correct, and if not, what I'm doing wrong. Thanks
Up until the very last step, the answer is 0.2/0.95=20/95 ~= 0.2105

CB

3. ## Re: Markov Chain Limiting Probabilities (Just need answer checked please)

Thank you very much