Question

Question 42(i)
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 is n(S)=1000
If the selected card has a perfect square greater than 500, then the player wins a prize.
Let $E_1$ =Event the first player wins a prize= Player select a card which is a perfect square greater than 500
={529, 576, 625, 729, 784, 841, 900, 961}
=$(23{)}^2,(24{)}^2,(25{)}^2,(26{)}^2,(27{)}^2,(28{)}^2,(29{)}^2,(30{)}^2,(31{)}^2$
$\therefore n\left(E_1\right)=9$
So, required probability=$\frac{n\left(E_1\right)}{n\left(S^{\prime }\right)}=\frac{9}{1000}=0.009$