2. Consider a diffusion model where the probability a molecule exits a cell in a one-second interval is $0.3$ while the probability it re-enters the cell in a one-second interval is $0.2$. Let $p_{t}$ be the probabilty the molecule is inside the cell at $t$ seconds for $t=0,1,2, \ldots$. (a) If the molecule starts inside, i.e. $p_{0}=1$, compute the probability the molecule is inside at $t+1, p_{t+1}$, in terms of $p_{t}$. (b) Find $p_{2}$, the probability the molecule is inside at $t=2$. (c) Find the probability the molecule is outside at $t=2$. (d) Compute the equilibrium of the system, which is the probability the molecule is inside "in the long run". SP.AS. 1215