The lemmings described in Section 6.2, Exercise 28, where a lemming has a probability 0.2 of jumping

Question:

The lemmings described in Section 6.2, Exercise 28, where a lemming has a probability 0.2 of jumping off the cliff each hour and a probability 0.1 of crawling back up.
Write the information from each of the following two-state Markov chains in terms of conditional probability. Write a discrete-time dynamical system for the probability, and find the long-term probability.