Given that \( x E[0,1] \) and \( y s[0,1] \). Let \( A \) be the event of \( (x, y) \) satisfyin...

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Given that \( x E[0,1] \) and \( y s[0,1] \). Let \( A \) be the event of \( (x, y) \) satisfying \( y^{2}x \) and \( B \) be the event of \( (x, y) \) satisfying \( x^{2}y \). Then
(a) \( P(A \cap B)=\frac{1}{3} \)
(b) A, B are exhaustive
(c) A, B are mutually exclusive
(d) A, B are independent
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