Optional stopping between +3 and −5

HardExpected Value Stochastic Processes~6m

A symmetric $\pm 1$ walk starts at $0$ and stops when it first hits $+3$ or $-5$ . Using the martingale $S_n$ and optional stopping, find the probability it hits $+3$ first. (to 3 decimals)

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$S_n$ is a martingale, so $E[S_\tau]=0$ .
Solve $3p - 5(1-p) = 0$ .

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0.625 (± 0.005)

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Optional stopping between +3 and −5

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