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Omni-MATH / A particular coin can land on heads (H), on tails (T), or in the middle (M), each with probability (1)/(3). Find the expected number of flips necessary to observe the contiguous se…

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problem

A particular coin can land on heads (H)(H), on tails (T)(T), or in the middle (M)(M), each with probability 13\frac{1}{3}. Find the expected number of flips necessary to observe the contiguous sequence HMMTHMMT...HMMT, where the sequence HMMT is repeated 2016 times.
Plain-text mathematical notation (without MathML)
A particular coin can land on heads (H), on tails (T), or in the middle (M), each with probability (1)/(3). Find the expected number of flips necessary to observe the contiguous sequence HMMTHMMT...HMMT, where the sequence HMMT is repeated 2016 times.
Original LaTeX notation
A particular coin can land on heads $(H)$, on tails $(T)$, or in the middle $(M)$, each with probability $\frac{1}{3}$. Find the expected number of flips necessary to observe the contiguous sequence HMMTHMMT...HMMT, where the sequence HMMT is repeated 2016 times.

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Source and history

task_id
7c383efb-389e-584a-8d46-1e9ecbe6c30f
task_key
test--7c383efb-389e-584a-8d46-1e9ecbe6c30f
task_revision_id
1
config / split
/ test

Official source

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