CBSE Class 10 Mathematics Probability MCQs Set 21

Download CBSE MCQs for Class 10 Mathematics: Chapter 14 Probability

Access targeted multiple-choice questions for Chapter 14 Probability designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Chapter-wise Objective Questions: Chapter 14 Probability

Navigate directly to the 50 objective questions for Chapter 14 Probability using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: A number is chosen at random from 1 to 100. The probability that it is a prime number is
(a) \( \frac{1}{5} \)
(b) \( \frac{6}{25} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{13}{50} \)
Show Answer & Explanation

Answer: (c) \( \frac{1}{4} \)

Explanation:
1. There are 25 primes up to 100.
2. P = 25/100 = 1/4.

Teacher's Note:
1. There are 25 primes below 100.
2. Remember that 1 is not prime.

Question 2: A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, the number of tickets she has bought is
(a) 40
(b) 240
(c) 480
(d) 750
Show Answer & Explanation

Answer: (c) 480

Explanation:
1. P = (her tickets)/6000 = 0.08.
2. Her tickets = 0.08 × 6000 = 480.

Teacher's Note:
1. Probability × total outcomes = favourable outcomes.
2. Check: 480/6000 = 0.08.

Question 3: A number x is chosen at random from −3, −2, −1, 0, 1, 2, 3. The probability that |x| < 2 is
(a) \( \frac{5}{7} \)
(b) \( \frac{3}{7} \)
(c) \( \frac{2}{7} \)
(d) \( \frac{1}{7} \)
Show Answer & Explanation

Answer: (b) \( \frac{3}{7} \)

Explanation:
1. |x| < 2 means x = −1, 0 or 1, so there are 3 favourable values.
2. P = 3/7.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 4: A card is drawn from a pack of 52 cards. The probability of getting a black ace is
(a) \( \frac{1}{52} \)
(b) \( \frac{1}{26} \)
(c) \( \frac{1}{13} \)
(d) \( \frac{1}{4} \)
Show Answer & Explanation

Answer: (b) \( \frac{1}{26} \)

Explanation:
1. There are 2 black aces (spades and clubs).
2. P = 2/52 = 1/26.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 5: A digit is chosen at random from the digits 1 to 9. The probability that it is even is
(a) \( \frac{4}{9} \)
(b) \( \frac{5}{9} \)
(c) \( \frac{1}{9} \)
(d) \( \frac{1}{2} \)
Show Answer & Explanation

Answer: (a) \( \frac{4}{9} \)

Explanation:
1. Even digits: 2, 4, 6, 8, so 4 favourable out of 9.
2. P = 4/9.

Teacher's Note:
1. Zero is not among 1 to 9, so there are only 9 outcomes.
2. Count even digits carefully.

Question 6: A letter of the English alphabet is chosen at random. The probability that it is a letter of the word 'RANDOM' is
(a) \( \frac{11}{26} \)
(b) \( \frac{3}{13} \)
(c) \( \frac{9}{26} \)
(d) \( \frac{4}{13} \)
Show Answer & Explanation

Answer: (b) \( \frac{3}{13} \)

Explanation:
1. The letters of RANDOM are R, A, N, D, O, M: 6 different letters.
2. P = 6/26 = 3/13.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 7: A bag contains 40 balls, some red, some blue and the rest black. If the probability of drawing a red ball is 11/20 and that of a blue ball is 1/5, the number of black balls is
(a) 5
(b) 25
(c) 10
(d) 30
Show Answer & Explanation

Answer: (c) 10

Explanation:
1. Red balls = 11/20 × 40 = 22 and blue balls = 1/5 × 40 = 8.
2. Black balls = 40 − 22 − 8 = 10.

Teacher's Note:
1. Alternatively P(black) = 1 − 11/20 − 1/5 = 1/4.
2. 1/4 of 40 = 10.

Question 8: Three unbiased coins are tossed. The probability of getting exactly two heads is
(a) \( \frac{1}{3} \)
(b) \( \frac{3}{4} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{3}{8} \)
Show Answer & Explanation

Answer: (d) \( \frac{3}{8} \)

Explanation:
1. Sample space has 2³ = 8 outcomes.
2. Exactly two heads: HHT, HTH, THH = 3 outcomes.
3. P = 3/8.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 9: Three unbiased coins are tossed. The probability of getting at most 2 heads is
(a) \( \frac{1}{4} \)
(b) \( \frac{3}{8} \)
(c) \( \frac{7}{8} \)
(d) \( \frac{1}{2} \)
Show Answer & Explanation

Answer: (c) \( \frac{7}{8} \)

Explanation:
1. Only HHH has more than 2 heads, so it is the only outcome not favourable.
2. P = 1 − 1/8 = 7/8.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 10: The probability that a number selected from the numbers 1, 2, 3, ..., 16 is a prime number is
(a) \( \frac{1}{16} \)
(b) \( \frac{5}{8} \)
(c) \( \frac{3}{8} \)
(d) \( \frac{7}{16} \)
Show Answer & Explanation

Answer: (c) \( \frac{3}{8} \)

Explanation:
1. Primes up to 16: 2, 3, 5, 7, 11, 13, which is 6 numbers.
2. P = 6/16 = 3/8.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 11: Tickets numbered 1 to 20 are mixed up and one is drawn at random. The probability that the number is a multiple of 3 is
(a) \( \frac{3}{20} \)
(b) \( \frac{3}{10} \)
(c) \( \frac{2}{5} \)
(d) \( \frac{1}{2} \)
Show Answer & Explanation

Answer: (b) \( \frac{3}{10} \)

Explanation:
1. Multiples of 3 up to 20: 3, 6, 9, 12, 15, 18, which is 6 numbers.
2. P = 6/20 = 3/10.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 12: One card is drawn at random from a pack of 52 cards. The probability that it is a face card is
(a) \( \frac{3}{13} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{9}{52} \)
(d) \( \frac{1}{13} \)
Show Answer & Explanation

Answer: (a) \( \frac{3}{13} \)

Explanation:
1. Face cards are jack, queen and king in each of 4 suits: 12 cards.
2. P = 12/52 = 3/13.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 13: The probability that an ordinary (non-leap) year has 53 Sundays is
(a) \( \frac{53}{365} \)
(b) \( \frac{1}{7} \)
(c) \( \frac{2}{7} \)
(d) \( \frac{48}{53} \)
Show Answer & Explanation

Answer: (b) \( \frac{1}{7} \)

Explanation:
1. An ordinary year has 365 days = 52 weeks + 1 extra day.
2. The extra day can be any of the 7 weekdays, and exactly one of them is a Sunday.
3. P = 1/7.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 14: In a simultaneous throw of two dice, the probability of getting a total of 7 is
(a) \( \frac{1}{6} \)
(b) \( \frac{7}{12} \)
(c) \( \frac{7}{36} \)
(d) \( \frac{1}{4} \)
Show Answer & Explanation

Answer: (a) \( \frac{1}{6} \)

Explanation:
1. Total outcomes = 36.
2. Pairs with sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6.
3. P = 6/36 = 1/6.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 15: In a simultaneous throw of two dice, the probability of getting a doublet is
(a) \( \frac{1}{6} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{3}{4} \)
(d) \( \frac{2}{3} \)
Show Answer & Explanation

Answer: (a) \( \frac{1}{6} \)

Explanation:
1. A doublet means both dice show the same number: (1,1), (2,2), ..., (6,6) = 6 outcomes.
2. P = 6/36 = 1/6.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 16: A bag contains 6 black and 8 white balls. One ball is drawn at random. The probability that the ball is white is
(a) \( \frac{4}{7} \)
(b) \( \frac{3}{4} \)
(c) \( \frac{4}{3} \)
(d) \( \frac{1}{8} \)
Show Answer & Explanation

Answer: (a) \( \frac{4}{7} \)

Explanation:
1. Total balls = 14 and white balls = 8.
2. P = 8/14 = 4/7.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 17: In a single draw from a pack of 52 cards, the probability of getting a king or a queen is
(a) \( \frac{1}{26} \)
(b) \( \frac{1}{13} \)
(c) \( \frac{2}{13} \)
(d) \( \frac{3}{13} \)
Show Answer & Explanation

Answer: (c) \( \frac{2}{13} \)

Explanation:
1. There are 4 kings and 4 queens, which are different cards, so 8 favourable cards.
2. P = 8/52 = 2/13.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 18: In a lottery there are 10 prizes and 25 blanks. The probability of getting a prize is
(a) \( \frac{1}{10} \)
(b) \( \frac{2}{5} \)
(c) \( \frac{2}{7} \)
(d) \( \frac{5}{7} \)
Show Answer & Explanation

Answer: (c) \( \frac{2}{7} \)

Explanation:
1. Total tickets = 10 + 25 = 35.
2. P = 10/35 = 2/7.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 19: An urn contains 9 red, 7 white and 4 black balls. A ball is drawn at random. The probability that it is not red is
(a) \( \frac{1}{11} \)
(b) \( \frac{9}{11} \)
(c) \( \frac{2}{11} \)
(d) \( \frac{11}{20} \)
Show Answer & Explanation

Answer: (d) \( \frac{11}{20} \)

Explanation:
1. Total = 20 balls, and balls that are not red = 7 + 4 = 11.
2. P = 11/20.

Teacher's Note:
1. Probability = favourable outcomes ÷ total outcomes.
2. List the sample space carefully before counting.

Question 20: A card is drawn from a pack of 52 cards. The probability that it is neither a heart nor a king is
(a) \( \frac{4}{13} \)
(b) \( \frac{9}{13} \)
(c) \( \frac{2}{13} \)
(d) \( \frac{1}{13} \)
Show Answer & Explanation

Answer: (b) \( \frac{9}{13} \)

Explanation:
1. Hearts: 13 cards. Kings: 4 cards, of which one (king of hearts) is also a heart.
2. Heart or king = 13 + 4 − 1 = 16, so neither = 52 − 16 = 36.
3. P = 36/52 = 9/13.

Teacher's Note:
1. Do not count the king of hearts twice.
2. Use the complement: 1 − 16/52.

Question 21: A card is drawn at random from a pack of 52 cards. The probability that it is a spade or a king is
(a) \( \frac{4}{13} \)
(b) \( \frac{3}{13} \)
(c) \( \frac{2}{13} \)
(d) \( \frac{1}{13} \)
Show Answer & Explanation

Answer: (a) \( \frac{4}{13} \)

Explanation:
1. Spades: 13 cards. Kings: 4 cards, with the king of spades counted in both.
2. Spade or king = 13 + 4 − 1 = 16.
3. P = 16/52 = 4/13.

Teacher's Note:
1. Subtract the overlap (king of spades) once.
2. Check by listing: 13 spades plus 3 other kings.

Question 22: What is the probability of getting two heads in four tosses of a coin?
(a) \( \frac{1}{2} \)
(b) \( \frac{3}{8} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{3}{16} \)
Show Answer & Explanation

Answer: (b) \( \frac{3}{8} \)

Explanation:
1. There are 2⁴ = 16 equally likely outcomes.
2. Outcomes with exactly two heads: C(4, 2) = 6.
3. P = 6/16 = 3/8.

Teacher's Note:
1. Exactly two heads means the other two are tails.
2. Count the arrangements with combinations.

Free study material for Mathematics

Multiple Choice Questions (MCQs) for Class 10 Mathematics Chapter 14 Probability

Class 10 Mathematics Chapter 14 Probability Objective Test Questions

Test your conceptual understanding of Chapter 14 Probability with these targeted multiple-choice questions. Designed in alignment with the latest CBSE curriculum for Class 10 Mathematics, these problem sets build accuracy and prepare students for objective exams.

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Cross-reference your completed choices with comprehensive NCERT solutions for Class 10 Mathematics to ensure absolute clarity across all sub-topics in this chapter.

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FAQs

Where can I access latest CBSE Class 10 Mathematics Probability MCQs Set 21?

You can get most exhaustive CBSE Class 10 Mathematics Probability MCQs Set 21 for free on StudiesToday.com. These MCQs for Class 10 Mathematics are updated for the 2026-27 academic session as per CBSE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 10 material?

Yes, our CBSE Class 10 Mathematics Probability MCQs Set 21 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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By solving our CBSE Class 10 Mathematics Probability MCQs Set 21, Class 10 students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.

Do you provide answers and explanations for CBSE Class 10 Mathematics Probability MCQs Set 21?

Yes, Mathematics MCQs for Class 10 have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused CBSE exams.

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