Class 10 Maths Chapter 15 Probability Practice Paper 2

PRACTICE PAPER 02 (2025-26) CHAPTER 14: PROBABILITY SUBJECT: MATHEMATICS STANDARD MAX. MARKS: 40 CLASS: X DURATION: 1½ hrs

General Instructions:

1. All questions are compulsory.

2. This question paper contains 20 questions divided into five Sections A, B, C, D and E.

3. Section A comprises of 10 MCQs of 1 mark each. Section B comprises of 4 questions of 2 marks each.

Section C comprises of 3 questions of 3 marks each. Section D comprises of 1 question of 5 marks and

Section E comprises of 2 Case Study Based Questions of 4 marks each.

4. There is no overall choice.

5. Use of Calculators is not permitted. SECTION – A Questions 1 to 10 carry 1 mark each.

1. A box contains 18 balls. Out of these, 6 are red, 8 are blue and 4 are green. If one ball is chosen randomly, what is the probability that it is neither red nor green?
(a) 1/3
(b) 4/9
(c) 5/9
(d) 2/3

2. Three unbiased coins are tossed together. The probability of getting exactly two heads is:
(a) 1/8
(b) 1/4
(c) 3/8
(d) 1/2

3. A card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card is a spade or an ace?
(a) 4/13
(b) 17/52
(c) 16/52
(d) 15/52

4. The probability that a student will pass the exam is 0.75. What is the probability that the student will fail?
(a) 0.25
(b) 0.5
(c) 0.75
(d) 1

5. A jar contains 24 marbles. Some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. How many blue marbles are in the jar?
(a) 6
(b) 8
(c) 12
(d) 16

6. If P(E) = 0.73, then what is the value of P(not E)?
(a) 0.27
(b) 0.37
(c) 0.63
(d) 0.73

7. A number x is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3. What is the probability that |x| < 2?
(a) 2/7
(b) 3/7
(c) 4/7
(d) 5/7

8. From a well-shuffled pack of cards, a card is drawn at random. Find the probability of getting a black face card.
(a) 1/26
(b) 3/26
(c) 3/13
(d) 1/2 In the following questions 9 and 10, a statement of assertion
(a) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion
(a) and reason (R) are true and reason (R) is the correct explanation of assertion
(a) .
(b) Both assertion
(a) and reason (R) are true but reason (R) is not the correct explanation of assertion
(a) .

(c) Assertion
(a) is true but reason (R) is false.
(d) Assertion
(a) is false but reason (R) is true.

9. Assertion
(a) : If two coins are tossed simultaneously, then the probability of getting no head is 1/4. Reason (R): The probability of getting a head in a single toss of a coin is 1/2.

10. Assertion
(a) : The probability of selecting a girl from a class of 10 boys and 15 girls is 3/5. Reason (R): P(girl) = Number of girls / Total students SECTION – B Questions 11 to 14 carry 2 marks each.

11. A box contains 90 discs numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears: (i) a two-digit number (ii) a number divisible by 6

12. All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Find the probability of getting: (i) a red card (ii) a card of hearts

13. A bag contains 3 red and 5 black balls. Another bag contains 4 red and 6 black balls. If one ball is drawn from each bag, find the probability that: (i) both balls are red (ii) both balls are black

14. It is given that the probability of winning a game is 0.7. What is the probability of losing the game? SECTION – C Questions 15 to 17 carry 3 marks each.

15. A bag contains white, black and red balls only. A ball is drawn at random from the bag. The probability of getting a white ball is 3/10 and that of a black ball is 2/5. Find the probability of getting a red ball. If the bag contains 20 black balls, find the total number of balls in the bag.

16. A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1, 2, 3, ..., 8 which are equally likely outcomes. What is the probability that the arrow will point at: (i) an odd number? (ii) a number greater than 3? (iii) a number less than 9?

17. A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that the ball drawn is:
(a) white?
(b) red?
(c) not white? SECTION – D Question 18 carries 5 marks.

18. A piggy bank contains hundred 50-paise coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the piggy bank is turned upside down, find the probability that the coin:
(a) will be a 50-paise coin
(b) will not be a ₹5 coin
(c) will be a ₹1 or ₹2 coin
(d) will be neither ₹2 nor ₹5 coin (e) will be a coin of value more than ₹1 SECTION – E (CASE STUDY BASED QUESTIONS) Questions 19 to 20 carry 4 marks each.

19. School Library Survey A survey was conducted in a school library to find out the reading preferences of students. Out of 200 students surveyed: 80 students prefer fiction books 50 students prefer non-fiction books 40 students prefer science magazines 30 students prefer comics Based on the above information, answer the following questions: (i) If a student is selected at random, what is the probability that the student prefers fiction books? (1) (ii) What is the probability that a randomly selected student does not prefer comics? (1) (iii)
(a) Find the probability that the student selected prefers either science magazines or comics. (1) OR
(b) Find the probability that the student selected prefers non-fiction books. (1) (iv) Which type of reading material is most preferred by students? What is the probability of selecting a student who prefers this type? (1)

20. Spinner Game In a school carnival, there is a circular spinner divided into 12 equal sectors numbered from 1 to 12. Players spin the arrow and win prizes based on where it stops. Prize rules: If the arrow stops at a prime number, the player wins ₹50 If the arrow stops at a perfect square, the player wins ₹100 If the arrow stops at a multiple of 4, the player wins ₹25 Based on the above information, answer the following questions: (i)
(a) What is the probability of winning ₹50? (1) OR
(b) What is the probability of winning ₹100? (1) (ii) What is the probability of winning ₹25? (1) (iii) What is the probability that a player does not win any prize? (Note: Consider that a number may satisfy more than one condition) (2) DETAILED ANSWER KEY

SECTION A - ANSWERS

1. Answer:
(b) 4/9

Solution:

Total balls = 18 Red balls = 6, Blue balls = 8, Green balls = 4 Neither red nor green means blue balls only P(blue ball) = 8/18 = 4/9

2. Answer:
(c) 3/8

Solution:

When three coins are tossed, total outcomes = 2³ = 8 Outcomes = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Exactly two heads: HHT, HTH, THH = 3 outcomes P(exactly two heads) = 3/8

3. Answer:
(a) 4/13

Solution:

Total cards = 52 Number of spades = 13 Number of aces = 4 Note: One ace is already counted in spades (Ace of Spades) Using: P(A or B) = P
(a) + P
(B) - P(A and B) Favorable cards = 13 + 4 - 1 = 16 P(spade or ace) = 16/52 = 4/13

4. Answer:
(a) 0.25

Solution:

P(pass) = 0.75 P(fail) = 1 - P(pass) = 1 - 0.75 = 0.25

5. Answer:
(b) 8

Solution:

Total marbles = 24 P(green) = 2/3 Number of green marbles = (2/3) × 24 = 16 Number of blue marbles = 24 - 16 = 8

6. Answer:
(a) 0.27

Solution:

P(E) = 0.73 P(not E) = 1 - P(E) = 1 - 0.73 = 0.27

7. Answer:
(b) 3/7

Solution:

Numbers: -3, -2, -1, 0, 1, 2, 3 (Total = 7 numbers) |x| < 2 means -2 < x < 2 Numbers satisfying this: -1, 0, 1 = 3 numbers P(|x| < 2) = 3/7

8. Answer:
(b) 3/26

Solution:

Total cards = 52 Black face cards = Jack, Queen, King of Spades and Clubs Number of black face cards = 3 + 3 = 6 P(black face card) = 6/52 = 3/26

9. Answer:
(b) Both assertion
(a) and reason (R) are true but reason (R) is not the correct explanation of assertion
(a) .

Solution:

Assertion
(a) is TRUE: When two coins are tossed, outcomes = {HH, HT, TH, TT} No head means TT = 1 outcome, so P = 1/4 Reason (R) is TRUE: P(head in single toss) = 1/2 However, R does not directly explain A. They are related but R is not the explanation of A.

10. Answer:
(a) Both assertion
(a) and reason (R) are true and reason (R) is the correct explanation of assertion
(a) .

Solution:

Total students = 10 boys + 15 girls = 25 P(girl) = 15/25 = 3/5 Assertion
(a) is TRUE: P(girl) = 3/5 Reason (R) is TRUE and correctly explains how to calculate P(girl)

SECTION B - ANSWERS

11. Solution: Discs numbered 1 to 90 = 90 discs (i) P(two-digit number): Two-digit numbers: 10, 11, 12, ..., 90 Count = 90 - 10 + 1 = 81 numbers P(two-digit) = 81/90 = 9/10 (ii) P(divisible by 6): Multiples of 6 from 1 to 90: 6, 12, 18, ..., 90 These form an AP with a = 6, d = 6, l = 90 Number of terms = (90 - 6)/6 + 1 = 15 P(divisible by 6) = 15/90 = 1/6

12. Solution: Face cards removed = 12 (4 jacks + 4 queens + 4 kings) Remaining cards = 52 - 12 = 40 (i) P(red card): Red face cards removed = 6 (3 hearts + 3 diamonds) Red cards remaining = 26 - 6 = 20 P(red card) = 20/40 = 1/2 (ii) P(card of hearts): Hearts face cards removed = 3 Hearts remaining = 13 - 3 = 10 P(hearts) = 10/40 = 1/4

13. Solution: Bag 1: 3 red + 5 black = 8 balls Bag 2: 4 red + 6 black = 10 balls (i) P(both balls are red): P(red from bag 1) = 3/8 P(red from bag 2) = 4/10 = 2/5 P(both red) = (3/8) × (2/5) = 6/40 = 3/20 (ii) P(both balls are black): P(black from bag 1) = 5/8 P(black from bag 2) = 6/10 = 3/5 P(both black) = (5/8) × (3/5) = 15/40 = 3/8

14. Solution: P(winning) = 0.7 P(losing) = 1 - P(winning) = 1 - 0.7 = 0.3 Therefore, probability of losing = 0.3

SECTION C - ANSWERS

15. Solution: P(white) = 3/10 P(black) = 2/5 = 4/10 P(white) + P(black) + P(red) = 1 3/10 + 4/10 + P(red) = 1 7/10 + P(red) = 1 P(red) = 1 - 7/10 = 3/10 Finding total balls: P(black) = Number of black balls / Total balls 2/5 = 20 / Total balls Total balls = 20 × 5/2 = 50 balls Therefore, P(red) = 3/10 and Total balls = 50

16. Solution: Numbers on board: 1, 2, 3, 4, 5, 6, 7, 8 Total outcomes = 8 (equally likely) (i) P(odd number): Odd numbers: 1, 3, 5, 7 = 4 numbers P(odd) = 4/8 = 1/2 (ii) P(number > 3): Numbers greater than 3: 4, 5, 6, 7, 8 = 5 numbers P(> 3) = 5/8 (iii) P(number < 9): All numbers (1 to 8) are less than 9 P(< 9) = 8/8 = 1 (sure event)

17. Solution: Total balls = 5 white + 7 red = 12 balls
(a) P(white): P(white) = 5/12
(b) P(red): P(red) = 7/12
(c) P(not white): P(not white) = 1 - P(white) = 1 - 5/12 = 7/12 Or, P(not white) = P(red) = 7/12

SECTION D - ANSWERS

18. Solution: Coins in piggy bank: • 50-paise coins = 100 • ₹1 coins = 50 • ₹2 coins = 20 • ₹5 coins = 10 Total coins = 100 + 50 + 20 + 10 = 180
(a) P(50-paise coin): P(50-paise) = 100/180 = 5/9
(b) P(not ₹5 coin): Coins that are not ₹5 = 180 - 10 = 170 P(not ₹5) = 170/180 = 17/18
(c) P(₹1 or ₹2 coin): ₹1 or ₹2 coins = 50 + 20 = 70 P(₹1 or ₹2) = 70/180 = 7/18
(d) P(neither ₹2 nor ₹5): Coins that are neither ₹2 nor ₹5 = 100 + 50 = 150 P(neither ₹2 nor ₹5) = 150/180 = 5/6 (e) P(value more than ₹1):

Coins worth more than ₹1 = ₹2 + ₹5 = 20 + 10 = 30 P(> ₹1) = 30/180 = 1/6

SECTION E - ANSWERS

19. School Library Survey - Solutions: Total students surveyed = 200 Fiction = 80, Non-fiction = 50, Science magazines = 40, Comics = 30 (i) P(fiction books): P(fiction) = 80/200 = 2/5 (ii) P(does not prefer comics): Students not preferring comics = 200 - 30 = 170 P(not comics) = 170/200 = 17/20 (iii)
(a) P(science magazines or comics): Students preferring science magazines or comics = 40 + 30 = 70 P(science magazines or comics) = 70/200 = 7/20 OR (iii)
(b) P(non-fiction books): P(non-fiction) = 50/200 = 1/4 (iv) Most preferred type:

Fiction books are most preferred with 80 students P(fiction) = 80/200 = 2/5

20. Spinner Game - Solutions: Numbers on spinner: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Total outcomes = 12 Analyzing the numbers: Prime numbers: 2, 3, 5, 7, 11 = 5 numbers (₹50 prize) Perfect squares: 1, 4, 9 = 3 numbers (₹100 prize) Multiples of 4: 4, 8, 12 = 3 numbers (₹25 prize) (i)
(a) P(winning ₹50): P(prime) = 5/12 OR (i)
(b) P(winning ₹100): P(perfect square) = 3/12 = 1/4 (ii) P(winning ₹25): P(multiple of 4) = 3/12 = 1/4 (iii) P(no prize): Numbers that win prizes: 1, 2, 3, 4, 5, 7, 8, 9, 11, 12 Note: 4 satisfies two conditions (perfect square AND multiple of 4) Numbers that don't win any prize: 6, 10 = 2 numbers P(no prize) = 2/12 = 1/6