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HMMT November 2010 E4

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An ant starts at the point (1,0)(1,0). Each minute, it walks from its current position to one of the four adjacent lattice points until it reaches a point (x,y)(x, y) with ∣x∣+∣y∣≥2|x|+|y| \geq 2. What is the probability that the ant ends at the point (1,1)(1,1) ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{7}{24}

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