Two persons \( A \) and \( B \) think of two numbers at random from...

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Two persons \( A \) and \( B \) think of two numbers at random from the numbers \( 1,2, \ldots, n \). Probability \( A \) think of a number smaller than thought by \( B \) is
(a) \( \frac{n-1}{2 n} \)
(b) \( \frac{2 n-1}{2 n} \)
(c) \( \frac{n-1}{2 n} \)
(d) \( \frac{n}{2 n-1} \)
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