question archive Suppose a groundhog jumps out of its hole (within a 1-minute interval) with probability 0

Suppose a groundhog jumps out of its hole (within a 1-minute interval) with probability 0

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Suppose a groundhog jumps out of its hole (within a 1-minute interval) with probability 0.2 and goes back inside (within a 1-minute interval) with probability 0.4. If the groundhog starts out inside the hole, answer the following questions.

(a) Let pt be the probability the groundhog is inside the hole after t minutes. Compute pt+1 in terms of pt .

(b) Find the probability the groundhog is outside after two minutes have passed.

(c) Find the long-run probability that the groundhog is inside, that is the equilibrium of the system

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