Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 5 / f / ii / Solution

The same geometric series identity givesA direct renewal check gives the identical result: $T_B={\tau }_B+T_I$ and $T_I={\tau }_I+q{T}_B$, so $p{T}_B={\tau }_B+{\tau }_I$. This also checks the units: mean first-passage time has units of time, unlike the dimensionless step count.