83. Exemplar Exercise Problem XXXXII

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?