Chapter 23 · Class 11-12 & JEE Main/Adv
Probability
40 topics in 13 parts
Classical Probability Probability Bounds Certain and Impossible Events Complement Rule Addition Rule Addition Rule for Mutually Exclusive Events
Key ideas
Analytical Comparison & Distinction Matrix
| Analytical Method | Standard Representation | Parametric / Invariant Framework |
|---|---|---|
| Algebraic Nature | Explicit equations relating spatial coordinates | Parameterized using scalar parameters (λ, μ) or vectors |
| Symmetry Usage | Relies on coordinate expansion | Exploits vector dot/cross products for rapid simplification |
| Computational Efficiency | Direct for intercept evaluation | Superior for angles, orthogonal projections, and distances |
| Common Mistake | Sign confusion in determinants | Omitting boundary condition checks |
All 40 topics in Probability
Definitions
- Sample Space & Events
- Random Experiment & Outcomes
- Simple & Compound Events
- Impossible & Sure Events
Algebra of Events
- Union & Intersection of Events
- Complementary Events
- Difference of Events (A but not B)
- Event of Neither A nor B
Different Types of Events
- Equally Likely Events
- Mutually Exclusive Events
- Exhaustive Events
Axiomatic Approach to Probability
- Axioms of Probability
- Basic Properties Derived from Axioms
Mathematical & Classical Definition of Probability
- Classical Definition of Probability
- Odds in Favour & Against an Event
- Combinatorial & Counting Problems
- Dice, Coin & Card Problems
- Integer & Selection Problems
Addition Theorem of Probability
- Theorem for Two & Three Events
- Principle of Inclusion-Exclusion in Probability
Independent Events
- Definition & Condition for Independent Events
- Pairwise & Mutual Independence
Compound & Conditional Probability
- Conditional Probability
- Multiplication Theorem of Probability
- Sampling With & Without Replacement
Total Probability Theorem
- Law of Total Probability
- Partition of Sample Space
- Tree Diagrams for Probability
Bayes' Theorem
- Standard Applications & Formula
- Extended Formula & Multiple Hypotheses
- Coincidence Testimony & Truth Speaking Problems
Geometrical Probability
- 1D & 2D Continuous Sample Spaces
- Area & Length Based Probabilities
Random Variable & Probability Distributions
- Discrete Random Variables
- Probability Mass Function (PMF)
- Mean & Variance of Distribution
- Expectation & Standard Deviation
Bernoulli Trials & Binomial Distribution
- Bernoulli Trials
- Binomial Distribution & Probabilities
- Mean & Variance of Binomial Distribution