# Probability of a disaster

Can you help me with this Markov chain problem? This should be simple, but my brain is not working well.

Let $\{{x_t}\}_{t=0}^\infty$ follows a Markov chain. Each $x_t$ can take two values: {G,B} (good or bad. bad represents a disaster). The transition probabilities are two unknowns:

Pr(G | G) = x

Pr(G | B) = y

You know the following:

-$x_0 = G$

-Expected duration of a disaster is d periods.

-The average frequency of disasters is f disasters per 100 periods

What are x and y?

Thank you.

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