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Omni-MATH / Two points are chosen inside the square {(x,y)∣0≤x,y≤1} uniformly at random, and a unit square is drawn centered at each point with edges parallel to the coordinate axes. The expec…

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problem

Two points are chosen inside the square {(x,y)∣0≤x,y≤1}\{(x, y) \mid 0 \leq x, y \leq 1\} uniformly at random, and a unit square is drawn centered at each point with edges parallel to the coordinate axes. The expected area of the union of the two squares can be expressed as ab\frac{a}{b}, where a,ba, b are relatively prime positive integers. Compute 100a+b100a+b.
Plain-text mathematical notation (without MathML)
Two points are chosen inside the square {(x,y)∣0≤x,y≤1} uniformly at random, and a unit square is drawn centered at each point with edges parallel to the coordinate axes. The expected area of the union of the two squares can be expressed as (a)/(b), where a,b are relatively prime positive integers. Compute 100a+b.
Original LaTeX notation
Two points are chosen inside the square $\{(x, y) \mid 0 \leq x, y \leq 1\}$ uniformly at random, and a unit square is drawn centered at each point with edges parallel to the coordinate axes. The expected area of the union of the two squares can be expressed as $\frac{a}{b}$, where $a, b$ are relatively prime positive integers. Compute $100a+b$.

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Source and history

task_id
aef15951-9090-5898-8f79-55b795c89641
task_key
test--aef15951-9090-5898-8f79-55b795c89641
task_revision_id
1
config / split
/ test

Official source

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