Six pieces, none past a half

HardProbability Random Variables~8m

A stick of length $1$ is cut at $5$ points chosen independently and uniformly along it, producing $6$ pieces. What is the probability that no piece is longer than $\tfrac12$ ?

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For $5$ uniform cuts, a given piece exceeds $t$ with probability $(1-t)^5$ .
Only one piece can exceed $1/2$ , so the six such events are disjoint: subtract $6\cdot(1/2)^5$ from $1$ .

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0.8125

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Asked at: Jane Street, Optiver

Six pieces, none past a half

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