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Omni-MATH / A fair coin is flipped eight times in a row. Let p be the probability that there is exactly one pair of consecutive flips that are both heads and exactly one pair of consecutive fl…

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problem

A fair coin is flipped eight times in a row. Let pp be the probability that there is exactly one pair of consecutive flips that are both heads and exactly one pair of consecutive flips that are both tails. If p=abp=\frac{a}{b}, where a,ba, b are relatively prime positive integers, compute 100a+b100a+b.
Plain-text mathematical notation (without MathML)
A fair coin is flipped eight times in a row. Let p be the probability that there is exactly one pair of consecutive flips that are both heads and exactly one pair of consecutive flips that are both tails. If p=(a)/(b), where a,b are relatively prime positive integers, compute 100a+b.
Original LaTeX notation
A fair coin is flipped eight times in a row. Let $p$ be the probability that there is exactly one pair of consecutive flips that are both heads and exactly one pair of consecutive flips that are both tails. If $p=\frac{a}{b}$, where $a, b$ are relatively prime positive integers, compute $100a+b$.

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task_id
6f00b999-1ae1-57af-880f-95534a2b25de
task_key
test--6f00b999-1ae1-57af-880f-95534a2b25de
task_revision_id
1
config / split
/ test

Official source

initial import