Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 9 / b / ii

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 givesSolving gives $t_1=t_3=7$ and $t_2=8$. Thus 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.