CBSE Class 10 Mathematics Probability MCQs Set 08

Download CBSE MCQs for Class 10 Mathematics: Chapter 14 Probability

Explore reliable objective questions for Chapter 14 Probability tailored for Class 10 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Chapter-wise Objective Questions: Chapter 14 Probability

View or download the dedicated Chapter 14 Probability MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question: Two dice are rolled together. The probability of getting sum of numbers on the two dice as \(2\), \(3\) or \(5\) is
(a) \(\frac{7}{36}\)
(b) \(\frac{11}{36}\)
(c) \(\frac{5}{36}\)
(d) \(\frac{4}{9}\)
Show Answer & Explanation

Answer: (a) \(\frac{7}{36}\)

Explanation:
1. Total outcomes \(= 36\).
2. Sum \(2\): \((1,1)\) — 1 way. Sum \(3\): \((1,2),(2,1)\) — 2 ways. Sum \(5\): \((1,4),(2,3),(3,2),(4,1)\) — 4 ways.
3. Favourable \(= 7\). Probability \(= \frac{7}{36}\).

Question: From the data \(1, 4, 7, 9, 16, 21, 25\), if all the even numbers are removed, the probability of getting at random a prime number from the remaining is
(a) \(\frac{2}{5}\)
(b) \(\frac{1}{5}\)
(c) \(\frac{1}{7}\)
(d) \(\frac{2}{7}\)
Show Answer & Explanation

Answer: (b) \(\frac{1}{5}\)

Explanation:
1. Remaining numbers: \(1, 7, 9, 21, 25\), so \(n(S) = 5\).
2. Only \(7\) is prime, so \(n(E) = 1\). Probability \(= \frac{1}{5}\).

Question: One card is drawn at random from a well shuffled deck of \(52\) playing cards. The probability that it is a red ace card is
(a) \(\frac{1}{13}\)
(b) \(\frac{1}{26}\)
(c) \(\frac{1}{52}\)
(d) \(\frac{1}{2}\)
Show Answer & Explanation

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

Explanation:
1. There are \(2\) red aces, so \(n(E) = 2\) and \(n(S) = 52\).
2. Probability \(= \frac{2}{52} = \frac{1}{26}\).

Question: A card is drawn at random from a well shuffled deck of \(52\) playing cards. The probability of getting a face card is
(a) \(\frac{1}{2}\)
(b) \(\frac{3}{13}\)
(c) \(\frac{4}{13}\)
(d) \(\frac{1}{13}\)
Show Answer & Explanation

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

Explanation:
1. There are \(12\) face cards. Probability \(= \frac{12}{52} = \frac{3}{13}\).

Question: A bag contains \(5\) pink, \(8\) blue and \(7\) yellow balls. One ball is drawn at random. The probability of getting neither a blue nor a pink ball is
(a) \(\frac{1}{4}\)
(b) \(\frac{2}{5}\)
(c) \(\frac{7}{20}\)
(d) \(\frac{7}{13}\)
Show Answer & Explanation

Answer: (c) \(\frac{7}{20}\)

Explanation:
1. Total balls \(= 20\). Neither blue nor pink means yellow: \(7\) balls.
2. Probability \(= \frac{7}{20}\).

Question: A number is chosen at random from \(1\) to \(15\). The probability that it is a multiple of \(4\) is
(a) \(\frac{4}{15}\)
(b) \(\frac{2}{15}\)
(c) \(\frac{1}{15}\)
(d) \(\frac{1}{5}\)
Show Answer & Explanation

Answer: (d) \(\frac{1}{5}\)

Explanation:
1. Multiples of \(4\): \(4, 8, 12\), so \(n(E) = 3\). \(n(S) = 15\).
2. Probability \(= \frac{3}{15} = \frac{1}{5}\).

Question: Two coins are tossed simultaneously. The probability of getting at most one head is
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{3}{4}\)
Show Answer & Explanation

Answer: (d) \(\frac{3}{4}\)

Explanation:
1. Outcomes: \(\{HH, HT, TH, TT\}\). At most one head: \(\{HT, TH, TT\}\), so \(n(E) = 3\).
2. Probability \(= \frac{3}{4}\).

Question: If an event cannot occur, then its probability is
(a) \(1\)
(b) \(\frac{3}{4}\)
(c) \(\frac{1}{2}\)
(d) \(0\)
Show Answer & Explanation

Answer: (d) \(0\)

Explanation:
1. An impossible event has probability \(0\).

Question: Which of the following cannot be the probability of an event?
(a) \(\frac{1}{3}\)
(b) \(0.1\)
(c) \(3\%\)
(d) \(\frac{17}{16}\)
Show Answer & Explanation

Answer: (d) \(\frac{17}{16}\)

Explanation:
1. A probability always lies between \(0\) and \(1\). \(\frac{17}{16} > 1\), so it cannot be a probability.

Question: If the probability of an event is \(p\), then the probability of its complementary event is
(a) \(p - 1\)
(b) \(p\)
(c) \(1 - p\)
(d) \(1 - \frac{1}{p}\)
Show Answer & Explanation

Answer: (c) \(1 - p\)

Explanation:
1. \(P(E) + P(\bar{E}) = 1\), so \(P(\bar{E}) = 1 - p\).

Question: The probability expressed as a percentage of a particular occurrence can never be
(a) less than \(100\)
(b) less than \(0\)
(c) greater than \(1\)
(d) anything but a whole number
Show Answer & Explanation

Answer: (b) less than \(0\)

Explanation:
1. A probability lies between \(0\) and \(1\), so as a percentage it lies between \(0\%\) and \(100\%\). It can never be less than \(0\).

Question: One ticket is drawn at random from a bag containing tickets numbered \(1\) to \(40\). The probability that the selected ticket has a number which is a multiple of \(5\) is
(a) \(\frac{1}{5}\)
(b) \(\frac{3}{5}\)
(c) \(\frac{4}{5}\)
(d) \(\frac{1}{3}\)
Show Answer & Explanation

Answer: (a) \(\frac{1}{5}\)

Explanation:
1. Multiples of \(5\) from \(1\) to \(40\): \(5, 10, \ldots, 40\), that is \(8\) numbers.
2. Probability \(= \frac{8}{40} = \frac{1}{5}\).

Question: If a letter is chosen at random from the letters of the English alphabet, the probability that it is a letter of the word DELHI is
(a) \(\frac{1}{5}\)
(b) \(\frac{1}{26}\)
(c) \(\frac{5}{26}\)
(d) \(\frac{21}{26}\)
Show Answer & Explanation

Answer: (c) \(\frac{5}{26}\)

Explanation:
1. Total letters \(= 26\). The word DELHI has \(5\) distinct letters.
2. Probability \(= \frac{5}{26}\).

Question: The probability that a two digit number selected at random will be a multiple of \(3\) and not a multiple of \(5\) is
(a) \(\frac{2}{15}\)
(b) \(\frac{4}{15}\)
(c) \(\frac{1}{15}\)
(d) \(\frac{4}{90}\)
Show Answer & Explanation

Answer: (b) \(\frac{4}{15}\)

Explanation:
1. There are \(90\) two-digit numbers. Multiples of \(3\): \(30\). Multiples of \(15\): \(6\).
2. Favourable \(= 30 - 6 = 24\). Probability \(= \frac{24}{90} = \frac{4}{15}\).

Question: In a lottery, there are \(5\) prizes and \(20\) blanks. The probability of getting a prize is
(a) \(\frac{2}{5}\)
(b) \(\frac{4}{5}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{1}{4}\)
Show Answer & Explanation

Answer: (c) \(\frac{1}{5}\)

Explanation:
1. Total tickets \(= 25\). Prizes \(= 5\). Probability \(= \frac{5}{25} = \frac{1}{5}\).

Question: The probability that the sum of the two numbers on two dice is a multiple of \(4\) is
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{8}\)
(d) \(\frac{1}{4}\)
Show Answer & Explanation

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

Explanation:
1. Sums that are multiples of \(4\): \(4, 8, 12\). Ways: \(3 + 5 + 1 = 9\).
2. Probability \(= \frac{9}{36} = \frac{1}{4}\).

Question: A letter is chosen at random from the letters of the word ASSASSINATION. The probability that the letter is a vowel is \(\frac{6}{2x + 1}\). Then \(x\) is equal to
(a) 5
(b) 6
(c) 7
(d) 8
Show Answer & Explanation

Answer: (b) 6

Explanation:
1. ASSASSINATION has \(13\) letters. Vowels: A, A, I, A, I, O — that is \(6\).
2. So \(\frac{6}{13} = \frac{6}{2x + 1}\), giving \(2x + 1 = 13\) and \(x = 6\).

Question: If \(P(E) + P(\bar{E})\) is considered, which of the following relationships is correct?
(a) \(P(\bar{E}) + P(E) = 1\)
(b) \(P(\bar{E}) - P(E) = 1\)
(c) \(P(\bar{E}) = 1 + P(E)\)
(d) None of these
Show Answer & Explanation

Answer: (a) \(P(\bar{E}) + P(E) = 1\)

Explanation:
1. For any event, \(P(E) + P(\bar{E}) = 1\).

Free study material for Mathematics

Practice MCQs for Class 10 Mathematics Chapter 14 Probability

Class 10 Mathematics Chapter 14 Probability Objective Test Questions

Review structured objective questions for Class 10 Mathematics Chapter 14 Probability. Built according to official CBSE guidelines, these MCQ sets support daily revision and core concept reinforcement.

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FAQs

Where can I access latest CBSE Class 10 Mathematics Probability MCQs Set 08?

You can get most exhaustive CBSE Class 10 Mathematics Probability MCQs Set 08 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 08 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

How do practicing Mathematics MCQs help in scoring full marks in Class 10 exams?

By solving our CBSE Class 10 Mathematics Probability MCQs Set 08, 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 08?

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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Yes, you can also access online interactive tests for CBSE Class 10 Mathematics Probability MCQs Set 08 on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.