State-Dependent Drift and First-Passage to a Boundary

A particle moves on $\{0, 1, 2, 3, 4\}$. From state $i$ ($0 < i < 4$), it jumps to $i+1$ with probability $p_i = i/4$ and to $i-1$ with probability $q_i = 1 - i/4$. States $0$ and $4$ are absorbing.

Starting from state $2$:

(a) Find the probability of being absorbed at state $4$.

(b) Find the expected number of steps until absorption (hitting either boundary).