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.
Choose one option. Section A of the board paper has 18 MCQs of 1 mark each, spread over all chapters.
A die is thrown once. The probability that the number shown is a perfect square is
Why: The perfect squares on a die are 1 and 4: 2 of 6 outcomes.
Favourable outcomes \(1\) and \(4\): \(P = \dfrac26 = \dfrac13\). (Remember that \(1 = 1^2\) is a perfect square.)
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
Why: Not red means blue or green: 5 of 10 balls.
\(P(\text{not red}) = \dfrac{3 + 2}{10} = \dfrac12\) (or \(1 - \dfrac{5}{10}\)).
For an event \(E\), \(P(E)\) is twice \(P(\text{not } E)\). Then \(P(E)\) is
Why: P(E) = 2(1 − P(E)) gives 3P(E) = 2.
\(P(\text{not } E) = 1 - P(E)\), so \(P(E) = 2(1 - P(E)) \Rightarrow 3P(E) = 2 \Rightarrow P(E) = \dfrac23\).
Only one of these numbers is a possible value for the probability of an event. Which one?
Why: A probability must lie between 0 and 1 inclusive.
\(0 \le P(E) \le 1\). \(-0.2 \lt 0\), while \(1.05\) and \(\dfrac76\) exceed \(1\); only \(\dfrac37\) is possible.
Three coins are tossed together. The probability of getting exactly two heads is
Why: Exactly two heads: HHT, HTH, THH — 3 of 8 outcomes.
The \(8\) outcomes are equally likely; \(HHT, HTH, THH\) have exactly two heads. \(P = \dfrac38\).
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
Why: 4 kings + 4 queens = 8 favourable cards.
\(P = \dfrac{4 + 4}{52} = \dfrac{8}{52} = \dfrac{2}{13}\).
Two dice are thrown together. The probability of getting the same number on both dice is
Why: There are 6 doublets among 36 outcomes.
Doublets \((1,1), (2,2), \ldots, (6,6)\): \(6\) of \(36\) outcomes, so \(P = \dfrac{6}{36} = \dfrac16\).
A number is chosen at random from \(1\) to \(60\). The probability that it is a perfect square is
Why: The squares are 1, 4, 9, 16, 25, 36, 49.
Perfect squares up to \(60\): \(1, 4, 9, 16, 25, 36, 49\) (seven; \(64 \gt 60\)). \(P = \dfrac{7}{60}\).
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
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 \(9\). \(P = \dfrac{9}{20}\).
A bag contains \(x\) red balls and \(12\) blue balls. If the probability of drawing a red ball is \(\dfrac14\), then \(x\) is
Why: x/(x + 12) = 1/4 gives 4x = x + 12.
\(\dfrac{x}{x + 12} = \dfrac14 \Rightarrow 4x = x + 12 \Rightarrow x = 4\).
A letter is chosen at random from the letters of the word MATHEMATICS. The probability that it is M is
Why: The word has 11 letters and M appears twice.
MATHEMATICS has \(11\) letters, of which \(2\) are M. \(P = \dfrac{2}{11}\).
Two dice are thrown together. What is the probability that the total shown is a multiple of \(5\)?
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 \(10\): \((4,6), (5,5), (6,4)\). \(P = \dfrac{7}{36}\).
Two dice are thrown together. The probability that the product of the numbers is \(6\) is
Why: Product 6 from (1,6), (6,1), (2,3), (3,2): 4 of 36.
Favourable: \((1,6), (6,1), (2,3), (3,2)\). \(P = \dfrac{4}{36} = \dfrac19\).
Three coins are tossed together. The probability of getting at most one head is
Why: At most one head: TTT, HTT, THT, TTH — 4 of 8 outcomes.
The \(8\) outcomes are equally likely. No head: \(TTT\); one head: \(HTT, THT, TTH\). \(P = \dfrac48 = \dfrac12\).
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
Why: 2 black aces + 2 red kings = 4 cards.
Black aces: spades and clubs (\(2\)); red kings: hearts and diamonds (\(2\)). \(P = \dfrac{4}{52} = \dfrac{1}{13}\).
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.
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.
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.
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 Essentials adds all 37 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 and the full common-mistakes library. There is no AI marking on CBSE Math Revision: you check your work against the marking scheme.
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 re-checked by computer algebra and 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.