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What is the probability that the first player wins a prize. 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

Solution:

Given, 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 square has a perfect square greater than 500, the player wins a prize.

We have to find the probability that the first player wins a prize.

Given, cards with numbers 1 to 1000.

Total number of cards = 1000

The probability that the first player wins a prize is given by

Favourable outcome = player selects a perfect square greater than 500.

Perfect square greater than 500 = {(23)², (24)², (25)², (26)², (27)², (28)², (29)², (30)², (31)²}

= {529, 576, 625, 676, 729, 784, 841, 900, 961}

Number of favourable outcomes = 9

Number of possible outcomes = 1000

Probability = number of favourable outcomes / number of possible outcomes

Probability = 9/1000

Therefore, the probability that the first player wins a prize is 9/1000.

✦ Try This: A bag contains 6 red, 3 black and 6 white balls. A ball is selected at random from the bag, what is the probability that the selected ball is white?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 42(i)

What is the probability that the first player wins a prize. 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

Summary:

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. The probability that the first player wins a prize is 9/1000

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