= Solution
Let $t_r$ be the <expected hitting time> of either absorbing state. The boundary values are $t_0=t_4=0$. The colour symmetry gives $t_1=t_3$, and <first-step analysis> gives
$$
t_1=1+\frac34t_2,\qquad t_2=1+\frac12t_1+\frac12t_3=1+t_1.
$$
Solving gives $t_1=t_3=7$ and $t_2=8$. Thus \b[the expected total number of draws from the stated initial condition is seven]. The additive one counts the current draw. Finiteness follows from the uniform two-step absorption bound in part (i), so the first-step equations do not hide an assumption of finite expectation.
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