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Probability

Average moves for a beetle to leave a strip

recursionfirst-step-analysisexpected-valuerandom-walk

A beetle stands on cell 2 of a strip of cells numbered 0 to 6. Each step it walks to an adjacent cell, right or left with equal probability 12\tfrac12. It leaves the strip when it reaches cell 0 or cell 6.

On average, how many steps does the beetle take before leaving?

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First-Step Analysis: Conditioning on What Happens NextWaiting Time Until a Pattern AppearsThe ABRACADABRA ProblemThe Card-Pack Trading GameCatalan Numbers

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