At a fete, cards bearing number 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 probability that
(i) the first player winz a price?
(ii) the second player wins a prize, if the first has won?

Explanation

Given that , at a fete, cards bearing number 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.
(i) Let `E_(1)`=Event first player winz a prize=Player select a card which is 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)}`
`therefore n(E_(1))=9`
`"So, required probability"=(nE_(1))/(n(S))=(9)/(1000)=0.009`
Let `E_(2)`= Event of the second player wins a prize, if the first has won. =Remaining cards has a perfect square greater than 500 are 8.
`therefore n(E_(2))=9-1=8`
So, required probability `(n(E_(1)))/(n(S'))=(8)/(999)`