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Omni-MATH / Starting with the number 0, Casey performs an infinite sequence of moves as…

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problem

Starting with the number 0, Casey performs an infinite sequence of moves as follows: he chooses a number from {1,2}\{1,2\} at random (each with probability 12\frac{1}{2}) and adds it to the current number. Let pmp_{m} be the probability that Casey ever reaches the number mm. Find p20−p15p_{20}-p_{15}.
Plain-text mathematical notation (without MathML)
Starting with the number 0, Casey performs an infinite sequence of moves as follows: he chooses a number from {1,2} at random (each with probability (1)/(2)) and adds it to the current number. Let p_(m) be the probability that Casey ever reaches the number m. Find p₂₀−p₁₅.
Original LaTeX notation
Starting with the number 0, Casey performs an infinite sequence of moves as follows: he chooses a number from $\{1,2\}$ at random (each with probability $\frac{1}{2}$) and adds it to the current number. Let $p_{m}$ be the probability that Casey ever reaches the number $m$. Find $p_{20}-p_{15}$.

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Source and history

task_id
6e38bdba-4d91-54f5-9a9f-4f70f1fda4c4
task_key
test--6e38bdba-4d91-54f5-9a9f-4f70f1fda4c4
task_revision_id
1
config / split
/ test

Official source

initial import