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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 greater than 500, the player wins a prize. What is the probability that the first player wins a prize?
Solution
Given that, 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 so, the total number of outcomes are n(S) = 1000
If the selected card has a perfect square greater than 500, then player wins a prize.
Let E1 = Event first player wins a prize
= Player select a card which is a perfect square greater than 500
= {529, 576, 625, 676, 729, 784, 841, 900, 961}
= {(23)2, (24)2, (25)2, (26)2, (27)2, (28)2, (29)2, (30)2, (31)2}
∴ n(E1) = 9
So, required probability = `(n(E_1))/(n(S)) = 9/1000` = 0.009
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