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Sometimes, probability questions can be interpreted geometrically, from simple examples like throwing darts to surprising applications like catching the bus!

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In the figure above, \(\square ABCD\) is a square with side length 1. Find the probability that \(\triangle PAB\) is an obtuse triangle, when \(P\) is a randomly chosen point inside \(\square ABCD.\)

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The figure above shows the base (of radius 11 cm) of a cylindrical bucket. There is a red circle of radius 4 cm centered at the center of the base. If Tom throws a coin of radius 1 cm into this bucket, what is the probability that the coin will land in contact with the perimeter of the red circle?

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