In Probability Class 12, questions are mostly application-based. The chapter includes conditional probability, Bayes’ theorem, random variables, and binomial distribution. These topics are regularly asked in CBSE Board exams. If your formulas are clear and the steps are written properly, this unit becomes scoring. What’s more, the same core ideas are also useful for the JEE Main 2026 exam, where probability appears under important topics.
Understanding the Base
Let’s start with the basics.
1. What is Probability?
Before moving to advanced problems, first understand what is probability.
Simply put, probability measures how likely an event is to occur. Its value lies between 0 and 1.
P(E)=Number of favourable outcomes / Total number of outcomes
For example, if a card is drawn from a deck of 52 cards, the probability of getting an Ace is 4/52 = 1/13, since there are 4 Aces.
Key facts for probability class 12:
- In case of an impossible event, Probability = 0
- In case of a certain event, Probability = 1
- The sum of probabilities of all outcomes is 1
These basics are used directly in conditional probability, the multiplication rule, and Bayes’ theorem.
Types of Probability
In probability and statistics, the commonly used types are:
- Theoretical probability
- Empirical probability
- Conditional probability
However, the CBSE Class 12 exam mainly focuses on conditional and distribution-based problems rather than theoretical discussion.
2. What is Statistics?
Now, what is statistics?
Statistics deals with collecting, organising, and analysing numerical data. In Class 12, the focus is limited and practical.
The fundamentals of statistics included in this unit are:
- Mean
- Variance
- Probability distributions
Probability helps calculate chances. Statistics help analyse values obtained from those probabilities. This connection becomes important in random variable questions.
Statistics & Probability for Class 12 Exam: Important Topics
Probability is one of the major topics of the CBSE Class 12 Mathematics syllabus.
| Unit | Included | Excluded |
| VI: Probability |
|
The variance of a random variable is excluded from theory questions. |
| Chapter Weightage: | 8 Marks |
Now, let’s focus on the areas that matter most for the Board exam
Important Topics
For Probability Class 12, the syllabus is limited but precise. These are the areas from which questions are directly asked in CBSE exams:
- Conditional Probability
- Multiplication Theorem
- Independent Events
- Theorem of Total Probability
- Bayes’ Theorem
- Random Variable
- Probability Distribution of a Random Variable
- Mean of a Random Variable
- Bernoulli Trials
- Binomial Distribution
These topics together form the complete probability and statistics portion prescribed for Class 12.
Statistics & Probability: Formulas
Once the topics are clear, the next step is to keep the required formulas organised in one place. Most mistakes in exams happen because students remember concepts but mix up formulas.
1. Probability Formulas
| Concept | Formula |
| Basic Probability | P(A)=Favourable outcomes / Total outcomes |
| Addition Rule | (I) For mutually exclusive
P (A B) = P(A)+P(B)$ (II) For non-mutually exclusive P (A B) = P (A)+P(B)-P(AB) |
| Multiplication Rule | For two independent events: P(AB)= P(A)P(B) |
| Conditional Probability | P (A | B) = P(AB)/ P (B)
(That is, Probability of A given B) |
| Bayes’ Theorem | P (A|B )= P (B|A) P(A) / P (B) |
| Binomial Probability | P (X = k) = nkpk (1- p)n-k where nkis binomial coefficient |
| Mean of Binomial | =np |
| Variance of Binomial | 2 = np (1-p) |
2. Statistics Formulas
These are the main statistics formulas used in random variable and distribution questions.
| Concept | Formula |
| Mean | Mean = x1+x2+x3+….+xnn |
| Median | Sum of two middle values / 2 |
| Variance | For a population: 2=1ni=1n (xi–)2
For a sample: s2=1n-1i=1n (xi–x)2 |
| Standard Deviation | = 2 or s = s2 |
Numericals
The formula alone doesn’t help until it is applied and practised thoroughly. In fact, the best way to revise the formulas is by solving typical exam-type numericals. The examples below follow standard Board patterns.
Example 1: Conditional Probability
In a class, 40% of students passed Mathematics, 30% passed Physics, and 20% passed both subjects. Find the probability that a student who passed Mathematics also passed Physics.
P(P|M) = P(P and M) / P(M)
= 0.20 / 0.40
= 0.5
Example 2: Independent Events
Two dice are thrown together. Find the probability that both show a 5.
Total possible outcomes = 6 × 6 = 36
Favourable outcome = (5,5)
Probability = 1 / 36
Since the outcome of one die does not affect the other, the events are independent.
Example 3: Mean of Random Variable
If a random variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3 respectively, find the mean.
Mean = 1(0.2) + 2(0.5) + 3(0.3)
= 0.2 + 1 + 0.9
= 2.1
Also Read :
- CBSE Class 12 Previous Years’ Question Papers with Solutions
- CBSE Class 12 Sample Papers for Board Exams
- CBSE Class 12 Maths Sample Question Papers with Solutions
- Class 12 Maths CBSE Board Latest Syllabus
Tips for This Chapter
After solving a few standard examples, preparation should move towards structured practice. Here are a few tips to help
- Write events clearly before applying any formula.
- Do not assume events are independent unless stated.
- In probability distribution questions, always check that the total probability equals 1.
- Show complete steps in Bayes’ theorem questions. Step marking matters.
- Revise all probability formulas class 12 weekly instead of before the exam.
- Practice full probability class 12 ncert solutions without skipping intermediate steps.
This chapter does not require lengthy theory. It requires accuracy and clear steps.
Conclusion
Probability class 12 is limited in syllabus but precise in application. Most Board questions are formula-based and predictable in pattern. If conditional probability, Bayes’ theorem, and distribution questions are practised properly, this unit becomes reliable for scoring.
Always remember, a clear understanding of probability and statistics concepts not only helps with the CBSE 12 boards exam, but it also prepares you for the JEE Main syllabus.
FAQs
1. Is probability a scoring chapter in Class 12 Maths?
Yes. Questions are mostly formula-based. With regular practice, this chapter can become a most reliable scoring point.
2. How important is Bayes’ theorem for Board exams?
Bayes’ theorem is frequently asked as a long-answer question. Clear stepwise working usually helps secure full marks.
3. What is the connection between probability and statistics in Class 12?
Probability calculates the chances of events, while statistics analyses numerical outcomes using the mean and distribution.
