CBSE Class 10 · Chapter 14 · Statistics and Probability · 2026-27

Probability Class 10: MCQ and case study questions

15 multiple-choice questions and 2 case-based questions on the current (rationalised) syllabus, in the style of the board paper's Sections A and E. Try each one first; the answer, a one-line reason and a worked solution open on a tap.

15 MCQs (1 mark each)
2 case studies (4 marks each)
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Multiple-choice questions

Tap an option to check it; the answer and a worked solution open. Section A of the board paper has 18 MCQs of 1 mark each, spread over all chapters.

Q1

·1 mark·Multiple choiceCoins and dice

A die is thrown once. The probability that the number shown is a perfect square is

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Answer: (b)

\frac{1}{3}

Why: The perfect squares on a die are 1 and 4: 2 of 6 outcomes.

Favourable outcomes $1$ and $4$ : $P = \frac{2}{6} = \frac{1}{3}$ . (Remember that $1 = 1^{2}$ is a perfect square.)

Q2

·1 mark·Multiple choiceClassical probability

A bag has $5$ red, $3$ blue and $2$ green balls. One ball is drawn at random. The probability that it is not red is

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Answer: (b)

\frac{1}{2}

Why: Not red means blue or green: 5 of 10 balls.

$P (not red) = \frac{3 + 2}{10} = \frac{1}{2}$ (or $1 - \frac{5}{10}$ ).

Q3

·1 mark·Multiple choiceComplementary events

For an event $E$ , $P (E)$ is twice $P (not E)$ . Then $P (E)$ is

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Answer: (c)

\frac{2}{3}

Why: P(E) = 2(1 − P(E)) gives 3P(E) = 2.

$P (not E) = 1 - P (E)$ , so $P (E) = 2 (1 - P (E)) \Rightarrow 3 P (E) = 2 \Rightarrow P (E) = \frac{2}{3}$ .

Q4

·1 mark·Multiple choiceClassical probability

Only one of these numbers is a possible value for the probability of an event. Which one?

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Answer: (d)

\frac{3}{7}

Why: A probability must lie between 0 and 1 inclusive.

$0 \leq P (E) \leq 1$ . $- 0.2 < 0$ , while $1.05$ and $\frac{7}{6}$ exceed $1$ ; only $\frac{3}{7}$ is possible.

Q5

·1 mark·Multiple choiceCoins and dice

Three coins are tossed together. The probability of getting exactly two heads is

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Answer: (b)

\frac{3}{8}

Why: Exactly two heads: HHT, HTH, THH — 3 of 8 outcomes.

The $8$ outcomes are equally likely; $H H T, H T H, T H H$ have exactly two heads. $P = \frac{3}{8}$ .

Q6

·1 mark·Multiple choicePlaying cards

A card is drawn at random from a well-shuffled pack of $52$ cards. The probability that it is a king or a queen is

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Answer: (a)

\frac{2}{13}

Why: 4 kings + 4 queens = 8 favourable cards.

$P = \frac{4 + 4}{52} = \frac{8}{52} = \frac{2}{13}$ .

Q7

·1 mark·Multiple choiceCoins and dice

Two dice are thrown together. The probability of getting the same number on both dice is

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Answer: (c)

\frac{1}{6}

Why: There are 6 doublets among 36 outcomes.

Doublets $(1, 1), (2, 2), \dots, (6, 6)$ : $6$ of $36$ outcomes, so $P = \frac{6}{36} = \frac{1}{6}$ .

Q8

·1 mark·Multiple choiceClassical probability

A number is chosen at random from $1$ to $60$ . The probability that it is a perfect square is

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Answer: (d)

\frac{7}{60}

Why: The squares are 1, 4, 9, 16, 25, 36, 49.

Perfect squares up to $60$ : $1, 4, 9, 16, 25, 36, 49$ (seven; $64 > 60$ ). $P = \frac{7}{60}$ .

Q9

·1 mark·Multiple choiceClassical probability

Twenty discs numbered $1$ to $20$ are put in a box and one is drawn at random. The probability that its number is a multiple of $3$ or of $5$ is

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Answer: (a)

\frac{9}{20}

Why: Multiples of 3: 6; of 5: 4; 15 is counted twice, so 9.

Multiples of $3$ : $3, 6, 9, 12, 15, 18$ ; of $5$ : $5, 10, 15, 20$ . Together (counting $15$ once) there are $9$ . $P = \frac{9}{20}$ .

Q10

·1 mark·Multiple choiceClassical probability

A bag contains $x$ red balls and $12$ blue balls. If the probability of drawing a red ball is $\frac{1}{4}$ , then $x$ is

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Answer: (b)

4

Why: x/(x + 12) = 1/4 gives 4x = x + 12.

$\frac{x}{x + 12} = \frac{1}{4} \Rightarrow 4 x = x + 12 \Rightarrow x = 4$ .

Q11

·1 mark·Multiple choiceClassical probability

A letter is chosen at random from the letters of the word MATHEMATICS. The probability that it is M is

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Answer: (c)

\frac{2}{11}

Why: The word has 11 letters and M appears twice.

MATHEMATICS has $11$ letters, of which $2$ are M. $P = \frac{2}{11}$ .

Q12

·1 mark·Multiple choiceCoins and dice

Two dice are thrown together. What is the probability that the total shown is a multiple of $5$ ?

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Answer: (a)

\frac{7}{36}

Why: Total 5 in 4 ways and total 10 in 3 ways: 7 of 36.

Total $5$ : $(1, 4), (2, 3), (3, 2), (4, 1)$ ; total $10$ : $(4, 6), (5, 5), (6, 4)$ . $P = \frac{7}{36}$ .

Q13

·1 mark·Multiple choiceCoins and dice

Two dice are thrown together. The probability that the product of the numbers is $6$ is

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Answer: (b)

\frac{1}{9}

Why: Product 6 from (1,6), (6,1), (2,3), (3,2): 4 of 36.

Favourable: $(1, 6), (6, 1), (2, 3), (3, 2)$ . $P = \frac{4}{36} = \frac{1}{9}$ .

Q14

·1 mark·Multiple choiceCoins and dice

Three coins are tossed together. The probability of getting at most one head is

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Answer: (d)

\frac{1}{2}

Why: At most one head: TTT, HTT, THT, TTH — 4 of 8 outcomes.

The $8$ outcomes are equally likely. No head: $T T T$ ; one head: $H T T, T H T, T T H$ . $P = \frac{4}{8} = \frac{1}{2}$ .

Q15

·1 mark·Multiple choicePlaying cards

One card is drawn at random from a well-shuffled pack of $52$ playing cards. The probability that it is either a black ace or a red king is

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Answer: (a)

\frac{1}{13}

Why: 2 black aces + 2 red kings = 4 cards.

Black aces: spades and clubs ( $2$ ); red kings: hearts and diamonds ( $2$ ). $P = \frac{4}{52} = \frac{1}{13}$ .

Case study questions

Section E of the board paper has three case-based questions of 4 marks: a real-life passage, then parts of 1, 1 and 2 marks, with a choice (OR) on the 2-mark part. All Class 10 case study questions by chapter.

Case study 1: Spin wheel at the school fete (4 marks)

At a school fete, a game stall has a spinning wheel divided into $12$ equal sectors numbered $1$ to $12$ . A player spins the wheel once, and it is equally likely to stop at any sector.

(i) Find the probability that the wheel stops at an even number. [1 mark]

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Answer:

\frac{1}{2}

Even numbers:

2, 4, 6, 8, 10, 12

;

P = \frac{6}{12} = \frac{1}{2}

. A1

(ii) Find the probability that it stops at a prime number. [1 mark]

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Answer:

\frac{5}{12}

Primes:

2, 3, 5, 7, 11

;

P = \frac{5}{12}

. A1

(iii) A player wins a prize if the number is greater than

8

or is a multiple of

4

. Find the probability of winning a prize. [2 marks]

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Answer:

\frac{1}{2}

Winning numbers:

4, 8, 9, 10, 11, 12

(

12

counted once) M1;

P = \frac{6}{12} = \frac{1}{2}

. A1

OR Find the probability that the number is a perfect square or a factor of

12

. [2 marks]

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Answer:

\frac{7}{12}

Perfect squares

1, 4, 9

; factors of

12

1, 2, 3, 4, 6, 12

. Together:

1, 2, 3, 4, 6, 9, 12

M1;

P = \frac{7}{12}

. A1

Case study 2: Class monitor by lottery (4 marks)

A class of $40$ students chooses one student at random to be the monitor for a week. The class has $18$ girls, $6$ of whom wear glasses; $10$ of the boys also wear glasses.

(i) Find the probability that the student chosen is a girl. [1 mark]

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Answer:

\frac{9}{20}

P = \frac{18}{40} = \frac{9}{20}

. A1

(ii) Find the probability that the student chosen wears glasses. [1 mark]

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Answer:

\frac{2}{5}

6 + 10 = 16

wear glasses;

P = \frac{16}{40} = \frac{2}{5}

. A1

(iii) Find the probability that the student chosen is a boy who does not wear glasses. [2 marks]

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Answer:

\frac{3}{10}

Boys

= 40 - 18 = 22

; without glasses

= 22 - 10 = 12

M1;

P = \frac{12}{40} = \frac{3}{10}

. A1

OR Four new girls, none of whom wear glasses, join the class before the draw. Find the new probability that the student chosen is a girl. [2 marks]

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Answer:

\frac{1}{2}

Girls

= 22

, class

= 44

M1;

P = \frac{22}{44} = \frac{1}{2}

. A1

Next steps for Probability

This free set is separate from the chapter's question bank. On the Probability chapter page the revision notes and the first step of the Route to 95 are free for everyone. CBSE Pro adds all 53 questions in the chapter bank (short and long answers, assertion–reason and more case studies) with their full step-marking schemes, the Route to 95 checkpoints with your progress saved, Skill Builders, the full common-mistakes library and AI marking of your written working.

Probability: important questions What Pro includes

Original questions written by CBSE Math Revision for the CBSE 2026-27 syllabus; not taken from NCERT, NCERT Exemplar or CBSE papers. Every answer was checked twice, the second time by an independent reviewer. CBSE Math Revision is independent and not affiliated with CBSE or NCERT. Spotted a slip? Tell us and it goes in the corrections log.