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Class 12 Mathematics — Chapter 13: Probability

66 practice questions · 22 Easy · 22 Medium · 22 Hard

Practise Class 12 Mathematics Chapter 13, "Probability", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.

"Probability" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.

Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Probability, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 12 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.

Key concepts: Probability (Class 12 Mathematics)

This chapter covers conditional probability, the multiplication theorem, independence, Bayes' theorem, and probability distributions of a random variable.

Conditional probability
P(A|B) = P(A∩B)/P(B), the probability of A given that B has occurred (P(B) ≠ 0).
Multiplication theorem
P(A∩B) = P(A)·P(B|A) = P(B)·P(A|B).
Independent events
A and B are independent if P(A∩B) = P(A)·P(B); then P(A|B) = P(A).
Bayes' theorem
Updates the probability of a cause given an observed effect, using prior probabilities and the theorem of total probability.
Random variable & distribution
A random variable assigns numbers to outcomes; its probability distribution lists values with probabilities and gives the mean (expectation).

Key formulas — Probability

Conditional probability
P(A|B) = P(A∩B) / P(B)
Bayes' theorem
P(Eᵢ|A) = P(Eᵢ)P(A|Eᵢ) / Σ P(Eⱼ)P(A|Eⱼ)
Mean of distribution
E(X) = Σ xᵢ·pᵢ

💡 Exam tips for Probability

  • Independence (P(A∩B)=P(A)P(B)) is not the same as mutually exclusive (P(A∩B)=0) — don't confuse them.
  • Bayes' theorem problems: identify the priors P(Eᵢ) and the likelihoods P(A|Eᵢ) clearly before substituting.

Sample questions

Q1Easy

P(A|B) =

A.P(A∩B)/P(B)✓ correct
B.P(A)/P(B)
C.P(A∪B)/P(B)
D.P(A)·P(B)
Why

Conditional probability.

Q2Medium

Bayes' theorem reverses:

A.Conditional probability direction (P(A|B) ↔ P(B|A))✓ correct
B.Sum into product
C.Mean and variance
D.Random
Why

Updates probabilities given evidence.

Q3Hard

Total probability theorem decomposes P(B) using:

A.Partition of sample space✓ correct
B.Differentiation
C.Limits
D.Integrals
Why

P(B) = Σ P(B|Aᵢ)P(Aᵢ).

Probability — FAQs

What are the key concepts in Class 12 Mathematics Probability?+

This chapter covers conditional probability, the multiplication theorem, independence, Bayes' theorem, and probability distributions of a random variable. Key ideas include Conditional probability, Multiplication theorem, Independent events, Bayes' theorem, Random variable & distribution.

What does Class 12 Mathematics Chapter 13 (Probability) cover on XamBaaz?+

It covers 66 NCERT-aligned MCQs on "Probability" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main and JEE Advanced.

Are these "Probability" questions free to practise?+

Yes — sign in with Google to practise "Probability" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.

How should I revise "Probability" for the exam?+

Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.

Practise all 66 questions free

Timed quizzes, instant scoring, streaks and XP. Sign in with Google — no card needed.

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