# What is the probability that the second player wins a prize, if the first has won. 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 second player wins a prize.

Given, cards with numbers 1 to 1000.

Total number of cards = 1000

The first player wins a prize by choosing a perfect square number.

The card is not replaced.

Remaining cards = 1000 - 1 = 999

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

Favourable outcome = player selects a perfect square greater than 500 except the card chosen by first player.

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 - 1 = 8

Number of possible outcomes = 999

Probability = number of favourable outcomes / number of possible outcomes

Probability = 8/999

Therefore, the probability that the second player wins a prize is 8/999

**✦ Try This: **A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.

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

**NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 42(ii)**

## What is the probability that the second player wins a prize, if the first has won. 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 first player wins a prize. The probability that the second player wins a prize is 8/999

**☛ Related Questions:**

- A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at rand . . . .
- A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at rand . . . .
- What is the probability that the first player wins a prize. At a fete, cards bearing numbers 1 to 10 . . . .

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