olymmath

HMMT November 2023 E9

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An entry in a grid is called a saddle point if it is the largest number in its row and the smallest number in its column. Suppose that each cell in a 3×33 \times 3 grid is filled with a real number, each chosen independently and uniformly at random from the interval [0,1][0,1]. Compute the probability that this grid has at least one saddle point.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3}{10}

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