Shortest of three pieces

HardProbability Random Variables~8m

A $1$ -metre stick is cut at two points chosen independently and uniformly along its length, giving three pieces. What is the probability that the shortest piece is at most $5$ centimetres (i.e. $\le 0.05$ m)?

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Use the complement: probability that all three pieces exceed $a=0.05$ .
For a stick cut at two uniform points, $\mathbb{P}(\text{all pieces}>a)=(1-3a)^2$ . Then subtract from $1$ .

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0.2775

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Asked at: Jane Street, Optiver

Shortest of three pieces

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