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?

Answer 1

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