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At a fete, cards bearing numbers \(1\) to \(1000\), one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than \(500\), the player wins a prize. What is the probability that
1. the first player wins a prize?
2. the second player wins a prize, if the first has won?
Answer:
The probability of the first player win's the prize is .
The probability of the second player win's the prize .
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