Markov Chains & Long-Run Behavior · Medium problem

A two-year college programme is modelled as an absorbing Markov chain. Each year a first-year student advances to second year with probability $0.7$, repeats first year with probability $0.1$, and drops out with probability $0.2$. A second-year student graduates with probability $0.8$, repeats second year with probability $0.1$, and drops out with probability $0.1$. Graduating and dropping out are absorbing. What is the probability that an entering first-year student eventually graduates? Express your answer as a common fraction.