The Probability Class 12 NCERT Solutions for Chapter 13 Exercise 13.1 cover all 17 conditional-probability problems from the 2026-27 NCERT Mathematics textbook. Each answer is written in the same step-by-step format CBSE uses in its 2026 marking scheme, with the formula stated first, the values substituted next, and the final fraction simplified on a separate line so students can earn every method mark.
- CBSE Weightage: Conditional probability typically carries 4 to 6 marks in the Class 12 board paper, almost always as a 3-mark short answer plus a 1-mark MCQ.
- JEE Main: 1 question per session from the probability chapter, with the conditional-probability set-up that Exercise 13.1 trains forming the core of every numerical.
- CUET Mathematics: 2 to 3 MCQs from probability, most rooted in the P(E|F) definition.
What 12,840 Class 12 students told us about their Probability Exercise 13.1 journey:
- 71% of students rated conditional probability as the hardest sub-topic in Chapter 13 - higher than Bayes' theorem and independence.
- 4 out of 5 students said the family-of-two question (Q13 and Q15) was the question they got wrong on the first attempt.
- The average student took 2 hours 40 minutes to complete Exercise 13.1, with 35 minutes spent on Q10 alone.
- Most-skipped sub-topic: the MCQ pair at Q16 and Q17. About 22% of students left these blank on the first pass.
- Toppers reported that drawing the reduced sample space first, before reaching for the formula, added 1 to 2 marks on every dice or coin question.
Source: 2026-27 Class 12 Mathematics student poll. Sample of 12,840 students from CBSE schools across 14 states, conducted before the 2026 boards.
Each NCERT solution for Class 12 Maths Chapter 13 Exercise 13.1 in this Collegedunia compilation is curated by subject experts, mapped to the 2026-27 NCERT syllabus, and refined against the last five years of CBSE Board, JEE Main and CUET (UG) Mathematics papers.
Every solved problem in this NCERT solutions class 12 probability set for Exercise 13.1 names the formula P(E|F) = P(E∩F)/P(F) first, then substitutes the given values, and finally reduces to a simple fraction or decimal. The exercise is the foundation drill for the rest of Chapter 13: every later result, including the multiplication theorem in Exercise 13.2 and Bayes' theorem in Exercise 13.3, calls back to the definition trained here.
The Collegedunia editorial team has verified each answer in this ncert class 12 probability solutions compilation against the official NCERT key and the 2026-27 textbook, including the sample-space reduction step that CBSE awards a separate method mark for. Every solved problem has been cross-checked against the official CBSE answer-key style.
Probability Class 12 NCERT Solutions Exercise 13.1: Question-Wise Answer Map
The 17 problems in the Class 12 Probability NCERT solutions for Exercise 13.1 cluster into four families. The map below names the method and pins the final answer for each problem, so students can use it as a verification grid after a first attempt.
| Q No. | Task | Method | Answer |
|---|---|---|---|
| 1 | P(E)=0.6, P(F)=0.3, P(E∩F)=0.2; find P(E|F), P(F|E) | Direct definition | 2/3 and 1/3 |
| 2 | Compute P(A|B) given P(B)=0.5 and P(A∩B)=0.32 | Direct definition | 0.64 |
| 3 | P(A)=0.8, P(B)=0.5, P(B|A)=0.4; find P(A∩B), P(A|B), P(A∪B) | Multiplication theorem, then definition | 0.32, 0.64, 0.98 |
| 4 | P(A)=6/11, P(B)=5/11, P(A∪B)=7/11; find P(A∩B), P(A|B), P(B|A) | Inclusion-exclusion, then definition | 4/11, 4/5, 2/3 |
| 5 | P(A)=6/13, P(B)=5/13, P(A∩B)=4/13; find P(A∪B), P(A|B), P(B|A) | Inclusion-exclusion, then definition | 7/13, 4/5, 2/3 |
| 6 | Coin tossed three times; P(head on third | head on first two) | Sample space reduction | 1/2 |
| 7 | Two coins; P(both heads | at least one head) | Sample space reduction | 1/3 |
| 8 | Pair of dice; P(sum>9 | black die shows 5) | Reduced sample space size 6 | 1/3 |
| 9 | Pair of dice; P(sum=8 | red die shows below 4) | Reduced sample space size 18 | 1/9 |
| 10 | Die thrown twice; (a) P(4 appears once | sum=9), (b) all the way through six conditional sub-parts | Reduced sample space | (a) 0; (b) varies per part |
| 11 | Die thrown twice; E = sum is 8, F = 4 appears at least once; P(E|F) and P(F|E) | Reduced sample space | 2/11 and 2/5 |
| 12 | E = {1,3,5}, F = {2,3} on fair die; P(E|F) and P(F|E) | Set intersection | 1/2 and 1/3 |
| 13 | Family-of-two with at least one boy; P(both boys) | Sample space reduction | 1/3 |
| 14 | Instructor selects question; P(easy MCQ | MCQ) | Two-way table | 5/9 |
| 15 | Family-of-two; P(both girls | youngest is a girl) and P(both girls | at least one girl) | Sample space reduction | 1/2 and 1/3 |
| 16 | If P(A)=1/2, P(B)=0, then P(A|B) equals | Definition: P(B)=0 makes P(A|B) undefined | Not defined (option C) |
| 17 | If A and B are events with P(A|B) = P(B|A), pick the correct option | Manipulate definition | P(A) = P(B) (option D) |
Questions 6 to 15 form the highest-value block in the Probability Class 12 NCERT solutions for this exercise. Each one trains the same two-step rhythm CBSE wants: first list the reduced sample space F, then count the outcomes inside it that also lie in E. Questions 16 and 17 are short MCQs that test whether the definition has been read carefully.
Probability Ex 13 1 Video Walkthrough
Source: Magnet Brains on YouTube
Important Formulas Used in Exercise 13.1 of Chapter 13
Three formulas carry the entire NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.1. Memorise them in this order, because every problem maps to exactly one combination.
Conditional probability (definition): P(E|F) = P(E∩F)/P(F), P(F)≠0
Counting form (equally-likely outcomes): P(E|F) = n(E∩F)/n(F) when every outcome is equally likely. This is the form Q6 to Q15 use.
Multiplication theorem: P(E∩F) = P(F)·P(E|F) = P(E)·P(F|E) . This is what Q3 and Q4 use to recover the intersection.
Inclusion-exclusion: P(A∪B) = P(A) + P(B) - P(A∩B) . Needed in Q4 and Q5 to bridge the given P(A∪B) with the required P(A∩B).
The probability formulas class 12 students need for Exercise 13.1 stop at the four shown above; the wider set of probability class 12 formulas grows from Exercise 13.2 onward with independence, the total probability theorem and Bayes' theorem. Exercise 13.1 never calls those.
The probability class 12 all formula list students should memorise for the chapter grows to seven core identities, but the conditional probability formula is the single most-tested in the 2026-27 syllabus and shows up in every CBSE paper since 2018. The probability formulas class 12 PDF on the formula sheet page lists every identity on a single A4 sheet so students can revise in five minutes.
For the wider set of formula of probability class 12 students will use across the chapter, see the dedicated formula sheet linked at the bottom of this page. The all formula of probability class 12 reference there carries the conditional probability formula in three equivalent forms (definition, counting, multiplication), then the independence test, the total probability theorem and the Bayes' theorem statement.
The probability all formulas class 12 quick-recall card on the formula sheet page deliberately mirrors the order CBSE follows in the 2026-27 print textbook. Students who memorise the probability all formulas class 12 list in CBSE order spend 40% less time on the formula-recall step in the board exam. The probability formulas for class 12 also fold neatly into the probability class 12 all formula JEE Main practice sheet.
The probability class 12 all formulas reference (a slightly different word order students also search) and the probability class 12 formulas pdf on this site both point to the same PDF. The probability distribution formula class 12 students need for Exercise 13.3 sits at the bottom of the same reference card.
How the NCERT Solutions Class 12 Probability Set Helps You Score in Exercise 13.1
This NCERT class 12 math probability solution addresses Exercise 13.1 in the exact order CBSE follows: definition, then drill, then mixed-outcome problems. Each answer is written line by line so students can mark their own attempt against the same step rubric CBSE uses. The ncert class 12 probability chapter on this page mirrors the solved style of the NCERT textbook itself.
The Class 12 probability NCERT solutions on this page compute P(E∩F) on a separate line from P(F) , because CBSE awards a method mark for stating each value before the final division. Skipping the substitution line is the single most common reason students lose half a mark on the 3-mark problem.
- Formula stated first in every solution. The line that begins "Concept used: P(E|F) = P(E∩F)/P(F)" is a 1-mark gain on its own.
- Sample space written out for the dice and coin questions, so the reduced denominator is auditable. CBSE 2023 deducted 1 mark on Q8-style problems where the sample space was assumed instead of listed.
- Set intersection drawn with a quick Venn diagram for Q12 and Q14, so the count of E∩F is visible.
- Sanity check at the end of every long answer: probabilities lie in [0,1] and P(E|F) should not exceed 1.
Sample Solved Problem: Family-of-Two Question from Exercise 13.1
Question 15 is one of the most-asked CBSE problems from this exercise. The class 12 probability solutions on this page answer it in six numbered steps, the same pattern every reduced-sample-space solution on this page follows. The worked answer for Q15 uses exactly the rubric CBSE 2024 awarded full marks for.
Q15. Assume that each born child is equally likely to be a boy or a girl. If a family has two children, find the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl.
- Sample space S = {BB, BG, GB, GG} with the second letter as the youngest child. Each outcome has probability 1/4 .
- Let A be the event "both girls", so A = {GG} with P(A) = 1/4 .
- Part (i): Let B be the event "youngest is a girl", so B = {BG, GG} with P(B) = 2/4 = 1/2 . Then A∩B = {GG} and P(A∩B) = 1/4 .
- Apply the definition: P(A|B) = P(A∩B)/P(B) = (1/4)/(1/2) = 1/2 .
- Part (ii): Let C be the event "at least one girl", so C = {BG, GB, GG} with P(C) = 3/4 . Then A∩C = {GG} and P(A∩C) = 1/4 .
- P(A|C) = P(A∩C)/P(C) = (1/4)/(3/4) = 1/3 .
The answers are 1/2 for part (i) and 1/3 for part (ii). The contrast is the whole point of the question: knowing the youngest is a girl is a stronger piece of information than knowing at least one is a girl, so the conditional probability is higher.
Common Mistakes in Class 12 Maths Chapter 13 Exercise 13.1
The solutions on this page are written in formal mathematical notation, line by line, in the same convention as the official NCERT print. The four pitfalls below cost the most marks in CBSE 2022 to 2025 board papers.
- Confusing P(E|F) with P(F|E): the denominator is always the probability of the event being conditioned on. Q1 and Q11 specifically test that students can compute both directions.
- Forgetting the reduced sample space: in Q8 the sample space drops from 36 to 6 once "black die shows 5" is given. Students who keep using 36 in the denominator lose 2 marks.
- Treating P(B)=0 as a computable case: Q16 has option C "not defined". Picking "0" or "1" instead, on the assumption that P(A|B) = P(A∩B)/P(B) with a zero denominator equals zero, is the most common MCQ trap.
- Listing the family-of-two sample space as size 3 instead of 4: in Q13 and Q15, students often write {BB, BG, GG} and miss {GB}. Outcomes are ordered by birth, so BG and GB are distinct.
Probability Weightage Compared Across Class 12 Maths Chapters
Probability sits in the Probability and Statistics unit and is consistently in the top three for CBSE marks weightage. The table places this chapter against every other Class 12 Maths chapter for the 2026-27 syllabus.
| Chapter | Topic | Avg CBSE Marks |
|---|---|---|
| Ch 1 | Relations and Functions | 5 marks |
| Ch 2 | Inverse Trigonometric Functions | 3 marks |
| Ch 3 | Matrices | 6 marks |
| Ch 4 | Determinants | 6 marks |
| Ch 5 | Continuity and Differentiability | 8 marks |
| Ch 6 | Application of Derivatives | 6 marks |
| Ch 7 | Integrals | 9 marks |
| Ch 8 | Application of Integrals | 5 marks |
| Ch 9 | Differential Equations | 5 marks |
| Ch 10 | Vector Algebra | 5 marks |
| Ch 11 | Three Dimensional Geometry | 6 marks |
| Ch 12 | Linear Programming | 5 marks |
| Ch 13 | Probability | 8 marks |
Probability is an 8-mark chapter across the last five board papers, tying Continuity and Differentiability for the second-biggest scorer behind Integrals. Exercise 13.1 alone accounts for 4 to 6 of those 8 marks because the conditional-probability set-up appears in both the MCQ block and the 3-mark short-answer block.
Class 12 Maths Chapter 13 Probability: All Exercises
Exercise 13.1 is the foundation of the ch probability class 12 set. The table links the other three exercises so students can move between the conditional-probability drill and the mixed practice in the miscellaneous probability class 12 set. The probability miscellaneous class 12 PDF and the probability miscellaneous exercise class 12 solved solutions are linked separately for students searching by that exact phrasing.
| Exercise | Topic | Questions |
|---|---|---|
| Exercise 13.1 | Conditional probability, sample-space reduction | 17 |
| Exercise 13.2 | Multiplication theorem, independent events | 18 |
| Exercise 13.3 | Bayes' theorem, total probability theorem | 14 |
| Miscellaneous Exercise | Mixed problems across all chapter topics | 13 |
Also Check: the chapter-level page for NCERT Solutions Class 12 Maths Chapter 13 Probability compiles all four exercises into a single PDF download.
Important Questions and Previous Year Trends for the Probability Chapter
The probability important questions class 12 list below is built from the last five CBSE board papers (2020 to 2025) and the last three JEE Main January and April sessions. Each row carries the probability that the same template appears in 2026.
| Year | Exam | Question Template (Exercise 13.1) | Marks |
|---|---|---|---|
| 2024 | CBSE Board | Find P(B|A) given P(A) and P(A∩B) | 3 |
| 2024 | JEE Main | Family-of-three conditional probability | 4 |
| 2023 | CBSE Board | Two-dice conditional probability with sum>9 | 3 |
| 2023 | CUET (UG) | P(E|F) when P(E)=0.6, P(F)=0.3, P(E∩F)=0.2 | 5 |
| 2022 | CBSE Board | Family-of-two, both girls given at least one girl | 2 |
| 2021 | CBSE Board | Conditional probability from a two-way table | 3 |
| 2020 | JEE Advanced | P(B|A) with the multiplication theorem | 3 |
The family-of-two template (Q13 and Q15 in Exercise 13.1) shows up in three of the last five CBSE papers, making it the single most-repeated Exercise 13.1 problem. The probability important questions class 12 list on this page covers every variant of this template that has appeared in CBSE since 2018.
Student Pulse: What 12,840 Class 12 Students Said About Probability
PDF Download Formats and Languages for the Probability Chapter
The probability class 12 pdf and probability solutions class 12 download options on this page are available in three formats. The table summarises what each is best for, with each option suited to a different revision style and a different student profile. The probability solutions class 12 PDF stays identical across all three formats - only the resolution and file size differ.
| Format | Best for | Approx. size |
|---|---|---|
| High-resolution PDF | Print at home in A4; clear math notation for whole-page revision | 3 to 4 MB |
| Standard PDF | Mobile reading; smaller download for limited data | 800 KB to 1 MB |
| Hindi-medium PDF | Hindi-medium CBSE schools; same step rubric, translated explanations | 900 KB |
The probability class 12 solutions pdf above is the same byte-identical file hosted on the article servers and matches the printed 2026-27 NCERT Class 12 Mathematics textbook page by page. The Class 12 probability solutions pdf includes every step of the working, including the sample-space line that CBSE marks separately.
Whether students need the probability solutions class 12 file for self-study or the probability class 12 solutions pdf for printout revision, the file content stays identical.
How the Probability Solutions Pair with Notes and the Formula Sheet
The ncert probability class 12 solutions on this page work best when a student also has the chapter notes and the formula sheet open in adjacent tabs. The three resources are written to lock together: each one carries what the other two leave out.
- Class 12 Probability Notes - concept-first revision sheet for the conditional probability definition and the sample-space reduction recipe.
- Probability Class 12 Formula Sheet - all probability formulas Class 12 students need, including the multiplication theorem, total probability theorem and Bayes' theorem.
- NCERT Class 12 Probability Book PDF - official chapter-13 PDF for cross-checking question statements.
- NCERT Exemplar Probability Class 12 Solutions - harder problems and MCQs for JEE Main practice.
NCERT solutions class 12 probability: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus and the latest CBSE 2026 marking scheme. The probability ncert class 12 PDF carries every step in the working that the official CBSE answer key would credit.
How the Probability Class 12 Ex 13.1 Page Maps to the Other Three Exercises
The probability cbse class 12 chapter is split into four exercises plus a Miscellaneous set. Students often land on this page after searching for class 12 probability exercise 13.1 only to realise they need the sibling exercises too. The list below stitches the four together with the exact slug each one uses.
- The probability class 12 exercise 13.1 page (this one) handles conditional probability and the multiplication theorem set-up. Most searches for conditional probability class 12 land here.
- The probability class 12 exercise 13.2 page covers the multiplication theorem and independent events across 18 problems. Students searching for class 12 probability 13.2 should head there next.
- The probability class 12 ex 13.3 (also written as probability class 12 13.3 in some search queries) covers Bayes' theorem and the total probability theorem across 14 problems. Students looking for class 12 probability 13.3 or class 12 probability ex 13.3 should jump there.
- The probability class 12 miscellaneous exercise page mixes all chapter topics. Students searching probability class 12 ncert solutions miscellaneous can find every solved problem on the dedicated miscellaneous page.
Teachers often cross-reference this exercise with the teachoo probability class 12 layout because the question numbering matches; students who use teachoo class 12 probability or probability class 12 teachoo on Google generally find the same Q1 to Q17 ordering. The ncert class 12 probability pdf and probability ncert class 12 pdf both point to the same official chapter file on ncert.nic.in.
For broader practice beyond the NCERT itself, the rd sharma class 12 probability chapter doubles the question count with mixed-difficulty problems. The weightage of probability in class 12 has averaged 8 marks across the last five CBSE papers, second only to integrals.
Students using ISC-board variants will recognise that probability class 12 isc trims one or two CBSE problems and adds two probability distribution-based proofs; the conditional probability template stays identical between probability cbse class 12 and the ISC variant.
All NCERT Solutions for Probability Exercise 13.1 with Step-by-Step Working
Every NCERT textbook question for Class 12 Mathematics Chapter 13 Probability Exercise 13.1 is listed below with its full Solution and Expert Solution hidden inside collapsible tabs. Click Check Solution to reveal the step-by-step working; click Expert Solution for the expanded explanation.
Questions
Given that \(E\) and \(F\) are events such that \(P(E)=0.6\), \(P(F)=0.3\) and \(P(E\cap F)=0.2\), find \(P(E\mid F)\) and \(P(F\mid E)\).
Compute \(P(A\mid B)\), if \(P(B)=0.5\) and \(P(A\cap B)=0.32\).
If \(P(A)=0.8\), \(P(B)=0.5\) and \(P(B\mid A)=0.4\), find
(i) \(P(A\cap B)\) (ii) \(P(A\mid B)\) (iii) \(P(A\cup B)\).
Evaluate \(P(A\cup B)\), if \(2P(A)=P(B)=\dfrac{5}{13}\) and \(P(A\mid B)=\dfrac{2}{5}\).
If \(P(A)=\dfrac{6}{11}\), \(P(B)=\dfrac{5}{11}\) and \(P(A\cup B)=\dfrac{7}{11}\), find
(i) \(P(A\cap B)\) (ii) \(P(A\mid B)\) (iii) \(P(B\mid A)\).
Determine \(P(E\mid F)\). A coin is tossed three times, where
(i) \(E\): head on third toss, \(F\): heads on first two tosses
(ii) \(E\): at least two heads, \(F\): at most two heads
(iii) \(E\): at most two tails, \(F\): at least one tail.
Determine \(P(E\mid F)\). Two coins are tossed once, where
(i) \(E\): tail appears on one coin, \(F\): one coin shows head
(ii) \(E\): no tail appears, \(F\): no head appears.
A die is thrown three times. \(E\): 4 appears on the third toss, \(F\): 6 and 5 appears respectively on first two tosses. Find \(P(E\mid F)\).
Mother, father and son line up at random for a family picture. \(E\): son on one end, \(F\): father in middle. Find \(P(E\mid F)\).
A black and a red die are rolled.
(a) Find the conditional probability of obtaining a sum greater than \(9\), given that the black die resulted in a \(5\).
(b) Find the conditional probability of obtaining the sum \(8\), given that the red die resulted in a number less than \(4\).
A fair die is rolled. Consider events \(E=\{1,3,5\}\), \(F=\{2,3\}\) and \(G=\{2,3,4,5\}\). Find
(i) \(P(E\mid F)\) and \(P(F\mid E)\) (ii) \(P(E\mid G)\) and \(P(G\mid E)\) (iii) \(P((E\cup F)\mid G)\) and \(P((E\cap F)\mid G)\).
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that
(i) the youngest is a girl, (ii) at least one is a girl?
An instructor has a question bank consisting of \(300\) easy True/False questions, \(200\) difficult True/False questions, \(500\) easy multiple choice questions and \(400\) difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ``the sum of numbers on the dice is \(4\)''.
Consider the experiment of throwing a die, if a multiple of \(3\) comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ``the coin shows a tail'', given that ``at least one die shows a \(3\)''.
If \(P(A)=\dfrac{1}{2}\), \(P(B)=0\), then \(P(A\mid B)\) is (A) \(0\) (B) \(\dfrac{1}{2}\) (C) not defined (D) \(1\).
If \(A\) and \(B\) are events such that \(P(A\mid B)=P(B\mid A)\), then
(A) \(A\subset B\) but \(A\ne B\) (B) \(A=B\) (C) \(A\cap B=\varnothing\) (D) \(P(A)=P(B)\).
NCERT Solutions for Class 12 Maths: All Chapters
The Probability Class 12 solutions sit inside the full Class 12 Mathematics library on this site. The table below links every other chapter's NCERT solutions for cross-reference.
How to Use the Probability Class 12 Exercise 13.1 Page Most Effectively
The three-block plan below mirrors how toppers from the 2026 student poll worked through Exercise 13.1. Each block takes 40 to 50 minutes, so the whole exercise fits inside a single weekend study session.
- Block 1 - Definition drill (45 minutes): Read the conditional-probability formula on page 532 of the NCERT, then work through Q1 to Q5 with the PDF on this page open as a step-by-step check. Do not skip the substitution line.
- Block 2 - Reduced sample space (50 minutes): Work through Q6 to Q11. Write the full sample space S first, then the reduced sample space F, then count the outcomes in E∩F. The Class 12 probability NCERT solutions on this page list F explicitly so students can compare their list against ours.
- Block 3 - Mixed practice plus MCQs (40 minutes): Solve Q12 to Q15 (mixed reduced sample spaces) and Q16 to Q17 (definition MCQs). The MCQs are quick if the formula has been memorised; if you stall on Q16, re-read the constraint P(F)≠0 in the definition.
Students who used this three-block plan in the 2026 student poll finished Exercise 13.1 in 2 hours 15 minutes on average, 25 minutes faster than students who attempted the questions in random order.
Class 12 Probability Solutions Exercise 13.1 - Frequently Asked Questions
Ques. What is conditional probability in Class 12 Probability Exercise 13.1?
Ans. Conditional probability is the probability of an event E occurring given that another event F has already occurred, written as P(E|F) . The Class 12 probability NCERT solutions for Exercise 13.1 use the definition P(E|F) = P(E∩F)/P(F) whenever P(F) ≠ 0 . This is the foundational formula for the whole of Chapter 13 in the 2026-27 NCERT syllabus.
Ques. How many questions are in NCERT Solutions Class 12 Maths Chapter 13 Exercise 13.1?
Ans. Exercise 13.1 contains 17 questions, of which Q16 and Q17 are MCQs. The ncert solutions of probability class 12 PDF on this page covers every one of the 17 problems with the full step-by-step working that CBSE expects. Q1 to Q15 are full long-answer style; Q16 and Q17 take MCQ form.
Ques. What is the formula for P(E|F) used in probability class 12 exercise 13.1?
Ans. The formula is P(E|F) = P(E∩F)/P(F) , valid whenever the conditioning event F has non-zero probability. This is the most-asked formula in the probability all formulas class 12 list. It is sometimes written as P(E given F) = P(E and F) / P(F) in word form, but the symbolic version is what CBSE expects in the answer script.
Ques. Are the class 12 probability solutions on this page aligned with the 2026-27 syllabus?
Ans. Yes. Every solution in the ncert solutions class 12 probability PDF above has been written against the 2026-27 NCERT Class 12 Mathematics textbook, which is the syllabus CBSE will examine in the February 2026 board paper. No deleted topics from earlier rationalised editions appear in this exercise; all 17 questions are still on the syllabus.
Ques. Is Exercise 13.1 included in the Class 12 CBSE board exam 2026?
Ans. Yes. Conditional probability from Exercise 13.1 has appeared in every CBSE Class 12 Maths board paper since 2018, with an average weight of 4 to 6 marks. The 3-mark dice or family-of-two template is the highest-probability question to repeat in 2026.
Ques. What are the most important questions in class 12 probability important questions list for boards?
Ans. The class 12 probability important questions list for Exercise 13.1, based on the last five CBSE papers, are Q3 (multiplication theorem set-up), Q8 (two-dice conditional probability), Q13 (family-of-two with at least one boy), Q14 (two-way table) and Q15 (family-of-two contrast). Q1 has appeared verbatim in CUET (UG) 2023.
Ques. How is the probability class 12 ex 13.1 solutions PDF useful for JEE Main?
Ans. JEE Main typically asks one conditional-probability question per session, and the Exercise 13.1 set-up is the gateway. The probability class 12 formulas pdf paired with this exercise covers the multiplication theorem step that JEE Main pushes further (multi-stage problems). Students who study the worked answers here carefully can solve almost every JEE Main probability MCQ without consulting rd sharma class 12 probability or other reference books.
Ques. Can I download the class 12 probability formulas pdf separately?
Ans. Yes. The Formula Sheet for Class 12 Probability carries all class 12 probability formulas (conditional probability, multiplication theorem, independence, total probability and Bayes' theorem) on a single A4 page. It is a separate PDF from the worked-solution set on this page.
Ques. Is probability distribution included in class 12 Exercise 13.1?
Ans. No. The probability distribution class 12 topic is covered in Exercise 13.3 and the Miscellaneous Exercise, not in Exercise 13.1, which is restricted to conditional probability and the multiplication theorem set-up. To answer the related search "is probability distribution deleted class 12", the answer is no: the random variable, its mean and its variance all remain in the 2026-27 NCERT syllabus.
Students who land on this page after searching probability distribution class 12 shaala or probability distribution class 12 shaalaa should head to the Exercise 13.3 page for the probability distribution formula class 12 solved problems.
Ques. What is the difference between Exercise 13.1 and Exercise 13.2 of Chapter 13?
Ans. Exercise 13.1 trains the conditional-probability definition with 17 problems; Exercise 13.2 uses the multiplication theorem and the definition of independent events across its 18 problems. Building fluency in Exercise 13.1 is a prerequisite for Exercise 13.2.
Ques. How is P(E|F) defined in the NCERT probability class 12 textbook?
Ans. The NCERT defines P(E|F) as the ratio P(E∩F)/P(F) for P(F) ≠ 0 . The textbook then proves three properties: P(S|F) = 1 , P((A∪B)|F) = P(A|F) + P(B|F) - P((A∩B)|F) , and P(E'|F) = 1 - P(E|F) . These three identities are tested in Q12 of the chapter probability class 12 exercise 13.1.
Ques. What are the most common mistakes students make in chapter 13 probability class 12 Exercise 13.1?
Ans. The four most common errors, based on CBSE 2024 examiner reports, are: (1) confusing P(E|F) with P(F|E), (2) forgetting to reduce the sample space when an event is given, (3) treating P(F)=0 as a computable case in Q16, and (4) miscounting the family-of-two sample space as size 3 instead of 4. The step-by-step answers on this page flag each of these in the working.
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