Why is $1/4$ the probability of hitting 6, starting in 0?

Question

We had the following Markov chain:

I cannot see the following statement:

Starting in 0, the probability of hitting 6 is $1/4$.

I do not see because what does this mean "hitting 6"? In how many steps?

Maybe you can explain.

With greetings

Answer 1

In infinitely many steps i suppose.

If you get to 4, you clearly get to 6, chances that this happens are:
After 1 step: 1/5
After 2 step: 1/5*1/5
After 3 step: 1/5*1/5*1/5

Do you understand now which infinite sum to look at?