Probability Class 12 Notes - Class 12 Maths Ch 13

This page hosts this chapter, presenting it for Class 12 Mathematics Chapter 13 Probability. These notes are sectioned to match the NCERT chapter, with each section closing in a short summary box and a single solved example. Suitable for both board and JEE Main preparation, the notes are free to download.

• CBSE Boards 2025: 8 to 10 marks, with one 5-mark Bayes question and one 2-mark conditional-probability item appearing in almost every set.
• JEE Main 2025: 2 to 3 questions per shift across Bayes, independence, and the Binomial distribution. Bayes is the single highest-yield sub-topic for JEE Main.

These Collegedunia this Class 12 page are cross-verified against the latest NCERT print, the CBSE 2025 marking scheme, and the JEE Main 2024 and 2025 answer keys. The numbered solved example inside every section mirrors the question style that examiners reward in board and JEE Main papers.

Also Check:

• Probability Class 12 Maths NCERT Solutions
• Probability Class 12 Maths Formula Sheet

Probability Video Walkthrough

Source: Magnet Brains on YouTube

Total Probability Theorem and Bayes' Theorem

Random Variables, Probability Distribution, Mean and Variance

A random variable assigns a real number to every outcome in the sample space. Its probability distribution lists each value x_i with probability p_i , subject to ∑ p_i = 1 .

The mean (expectation) is E(X) = ∑ x_i p_i . The variance is Var(X) = E(X²) - [E(X)]² , and the standard deviation is its positive square root.

Previous Year Trend: Probability in CBSE and JEE Main

The table tracks the appearance and mark-weight of each sub-topic across the past five years of CBSE Class 12 Maths and JEE Main. Bayes' theorem and the Binomial distribution share the top spot; conditional probability never drops below 2 marks in any board paper.

Full year-wise PYQ map: the chapter notes NCERT Solutions.

How Will Collegedunia's Probability Notes Help You Score Higher?

These Collegedunia notes are calibrated to the way CBSE and JEE Main actually frame Probability questions. The Bayes section walks through the urn-factory-test template that has appeared in 9 of the past 10 board papers.

The Binomial section ends with the three trial-condition checks that catch the 90% of students who misapply the formula to a sampling-without-replacement setup. Every formula sits beside the question pattern that uses it, so reading these notes once is equivalent to drilling 20 mixed problems.

Common Mistakes Students Make When Using the Probability Class 12 Notes

• probability Notes
• Treating mutually exclusive events as independent. They are independent only when at least one has zero probability.
• Forgetting the weights p_i in the variance formula and computing ∑ (x_i - μ)² instead.
• Applying the Binomial PMF to sampling without replacement.
• Confusing the prior P(A_i) with the posterior P(A_i | E) in a Bayes setup.
• Dropping the conditioning event in P(A | B) + P(A' | B) = 1 and writing P(A) + P(A') instead.

Other Resources for Class 12 Maths Chapter 13 Probability

• this Class 12 page NCERT Solutions
• the resource Formula Sheet
• the chapter notes Handwritten Notes
• the PDF Exemplar Solutions

NCERT Notes for Class 12 Maths: All Chapters

The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.

this Class 12 page: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.

Probability Class 12 Notes - Quick Summary

• The the resource cover every section of Class 12 Mathematics Chapter 13 Probability, aligned to the 2026-27 NCERT print.
• The chapter notes include formal definitions, solved examples and end-of-section formula recap suitable for board and JEE Main preparation.
• The the PDF are downloadable as a free PDF and follow the notation of the official NCERT textbook line for line.

Exercise-wise Breakdown of the Probability Chapter

The Probability chapter splits into 3 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.

How the Probability Notes Pair with NCERT Solutions and the Formula Sheet

The Probability Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:

Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.

• The this Class 12 page ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
• The probability class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
• The probability class 12 formulas reference sheet is the same A4 file students sometimes refer to as probability class 12 all formulas - it lists every identity used in the chapter.
• State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board the resource textbook PDF all share the same core definitions.
• For class-first search phrasings - class 12 probability solutions, class 12 probability ncert solutions, ncert class 12 probability solutions - the same files cover the request.

Reference Books and State-Board Mapping

Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly: