Matching bolts and nuts have the diameters (X) and (Y), respectively. The random vector ((X, Y)) has

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Matching bolts and nuts have the diameters \(X\) and \(Y\), respectively. The random vector \((X, Y)\) has a uniform distribution in a circle with radius \(1 \mathrm{~mm}\) and midpoint (30mm , 30mm). Determine the probabilities

(1) \(P(Y>X)\), and (2) \(P(Y \leq X<29)\).

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