Biased Random Walk Reaching Position 1
A particle starts at position $0$ on the integer number line. At each step, it moves right (from $i$ to $i+1$) with probability $p$ and left (from $i$ to $i-1$) with probability
- p$.
If $p = 3/4$, what is the probability the particle ever reaches position
$?
For full credit, derive the answer for general $p$ and then specialize.
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