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  • 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 pr

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

(i) the first player wins a prize?
(ii) the second player wins a prize, if the first has won?

 

Answers (1)

(i) Answer.  [0.009]
Solution. Probability; Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Total cards = 1000
Player wins prize with cards = (529, 576, 625, 676, 729, 784, 841, 900, 961)
  Favourable cases = 9
Probability = \frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}
Probability that player wins = \frac{9}{1000}= 0\cdot 009

 (ii) Answer. [0.008]
Solution. Probability; Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Now the total cards are = 1000 – 1 = 999
Now the total winning cards = 9 – 1 = 8
Probability = \frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}
Probability that second player wins after first = \frac{8}{999}\approx 0\cdot 008
 

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