Landing two above the start

EasyStochastic Processes~2m

A simple symmetric random walk starts at 0 and takes steps of $\pm1$ . What is the probability it is at position $+2$ after exactly 6 steps? Give a decimal to four places.

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Solve $2u-6=2$ for the number of up-steps $u$ .
Then $P=\binom{6}{u}/2^6$ .

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0.2344 (± 0.001)

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Asked at: Game-Based Aptitude, EV & Betting Games

Landing two above the start

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