Absorption probability on a line

MediumProbability Stochastic Processes~4m

A token sits at position $2$ on $\{0,1,2,3,4\}$ . Each step it moves $\pm 1$ with equal probability; $0$ and $4$ are absorbing. What is the probability it is absorbed at $4$ ? (to 3 decimals)

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Absorption probability is harmonic, hence linear, in position.
$P = (\text{start})/(\text{right barrier})$ .

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0.5 (± 0.005)

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Absorption probability on a line

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