Question

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 number greater than 500, the player wins a prize. What is the probability that the second player wins a prize if the first has won?

Answer 1

22² = 484

31² = 961

23² = 529

32² = 1024

23, 24, 25, 26, 27, 28, 29, 30, 31 has squares below 500 × 1000.

P(second player wins if first has won) =  `8/999`