eVidyarthi

Main Menu
  • eVidyarthi
  • School
    • Class 6th
      • Maths Class 6
      • Science Class 6
      • Hindi Class 6
      • व्याकरण
      • English Class 6
      • English Grammar
      • Sanskrit Class 6
      • Geography
      • Civics
      • History
    • Class 7th
      • Maths Class 7
      • Science Class 7
      • Hindi Class 7
      • व्याकरण
      • English Class 7
      • English Grammar
      • Sanskrit Class 7
      • Geography
      • Civics
      • History
    • Class 8th
      • Maths Class 8
      • Science Class 8
      • Hindi Class 8
      • व्याकरण
      • English Class 8
      • English Grammar
      • Sanskrit Class 8
      • Geography
      • Civics
      • History
    • Class 9th
      • Maths Class 9
      • Science Class 9
      • Hindi Class 9
      • English Class 9
      • English Grammar
      • व्याकरण
      • Economics Class 9
      • Geography Class 9
      • Civics Class 9
      • History Class 9
    • Class 10th
      • Maths Class 10
      • Science Class 10
      • Hindi Class 10
      • English Class 10
      • English Grammar
      • व्याकरण
      • Economics Class 10
      • History Class 10
      • Civics Class 10
      • Geography Class 10
    • Class 11th
      • Maths Class 11
      • Accounts Class 11
      • English Class 11
      • English Grammar
      • व्याकरण
      • Chemistry Class 11
      • Physics Class 11
      • Biology Class 11
    • Class 12th
      • Maths Class 12
      • Accounts Class 12
      • Chemistry Class 12
      • Physics Class 12
      • Biology Class 12
      • English Class 12
      • English Grammar
      • व्याकरण
    • Close
  • English
    • Basic English Grammar
    • Basic English Speaking
    • English Vocabulary
    • English Idioms & Phrases
    • Personality Enhancement
    • Interview Skills
    • Close
  • Softwares
    • Microsoft Word
    • PhotoShop
    • Excel
    • Illustrator
    • PowerPoint
    • Close
Class 11th Maths || Menu
  • Important
    • Sample Papers
    • MCQs
    • Important Formulas
    • Revision Notes
    • Mathematics Syllabus
    • Mathematics Book
    • Close
  • Sets
    • Set Notations
    • Subsets and Supersets
    • Operations on Sets
    • Algebra of Sets
    • Counting Theorems
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Relations and Functions
    • Cartesian Product of Sets
    • Relations
    • Functions
    • Graphs and Algebra of Functions
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Trigonometric Functions
    • Ex 3.1
    • Ex 3.2
    • Ex 3.3
    • Ex 3.4
    • Examples
    • MCQs
    • Miscellaneous Exercises
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Principle of Mathematical Induction
    • Ex 4.1
    • Examples
    • MCQs
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Complex Numbers and Quadratic Equations
    • Introduction to Complex Numbers
    • Geometry of Complex Numbers
    • Quadratic Equations
    • Square Root of A Complex Number
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Linear Inequalities
    • Linear Inequalities : One Variable
    • Linear Inequalities : 1 and 2 Variables
    • Graphical Solutions
    • Word Problems : Linear Inequalities
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Permutations and Combinations
    • Fundamental Principle of Counting
    • Permutations: Distinct Objects
    • Permutations: Non Distinct Objects
    • Combinations
    • Applications of Permutations and Combinations
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Binomial Theorem
    • Binomial Theorem for Positive Index
    • General Terms in Binomial Expansion
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Sequence and Series
    • Arithmetic Progressions
    • Arithmetic Mean
    • Geometric Progressions
    • Special Sequences and Series
    • Relation Between AM and GM
    • Introduction to Sequences
    • Sum to Infinity of A GP
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Straight Lines
    • Basic Concepts of 2D Geometry
    • Various Forms of Equation of A Line
    • Slope of A Line
    • Distance Between Lines
    • Normal and General Form of A Line
    • Shifting of Origin
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Conic Sections
    • Circles
    • Parabola
    • Ellipse
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Introduction To Three Dimensional Geometry
    • Introduction to 3-D Geometry
    • Distance Formula:3-D Geometry
    • Section Formula: 3- D Geometry
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Limits And Derivatives
    • Introduction and Algebra of Limits
    • Limits of Rational Functions
    • Limits of Trigonometric Functions
    • Sum and Difference Rule
    • Product and Quotient Rule
    • Infinite Limits
    • Meaning of Derivatives
    • Logarithmic and Exponential Limits
    • NCERT Solutions
    • Close
  • R.D Sharma Solutions
  • Mathematical Reasoning
    • Mathematical Statements
    • Implications and Validating of Statements
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close
  • Statistics
    • Mean Deviation
    • Variance and Standard Deviation
    • NCERT Solutions
    • Close
  • Probability
    • Introduction to Probability
    • Axiomatic Probability
    • Problems on Probability
    • NCERT Solutions
    • R.D Sharma Solutions
    • Close

CBSE Class 11 Maths Chapter 16 Probability Notes

Random Experiment
An experiment whose outcomes cannot be predicted or determined in advance is called a random experiment.

Outcome
A possible result of a random experiment is called its outcome.

Sample Space
A sample space is the set of all possible outcomes of an experiment.

Events
An event is a subset of a sample space associated with a random experiment.

Types of Events
Impossible and sure events: The empty set Φ and the sample space S describes events. Intact Φ is called the impossible event and S i.e. whole sample space is called sure event.

Simple or elementary event: Each outcome of a random experiment is called an elementary event.

Compound events: If an event has more than one outcome is called compound events.

Complementary events: Given an event A, the complement of A is the event consisting of all sample space outcomes that do not correspond to the occurrence of A.

Mutually Exclusive Events
Two events A and B of a sample space S are mutually exclusive if the occurrence of any one of them excludes the occurrence of the other event. Hence, the two events A and B cannot occur simultaneously and thus P(A ∩ B) = 0.

Exhaustive Events
If E1, E2,…….., En are n events of a sample space S and if E1 ∪ E2 ∪ E3 ∪………. ∪ En = S, then E1, E2,……… E3 are called exhaustive events.

Mutually Exclusive and Exhaustive Events
If E1, E2,…… En are n events of a sample space S and if
Ei ∩ Ej = Φ for every i ≠ j i.e. Ei and Ej are pairwise disjoint and E1 ∪ E2 ∪ E3 ∪………. ∪ En = S, then the events
E1, E2,………, En are called mutually exclusive and exhaustive events.

Probability Function
Let S = (w1, w2,…… wn) be the sample space associated with a random experiment. Then, a function p which assigns every event A ⊂ S to a unique non-negative real number P(A) is called the probability function.
It follows the axioms hold

  • 0 ≤ P(wi) ≤ 1 for each Wi ∈ S
  • P(S) = 1 i.e. P(w1) + P(w2) + P(w3) + … + P(wn) = 1
  • P(A) = ΣP(wi) for any event A containing elementary event wi.

Probability of an Event
If there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of occurrence of A is defined as
Probability Class 11 Notes Maths Chapter 16

The odd in favour of occurrence of the event A are defined by m : (n – m).
The odd against the occurrence of A are defined by n – m : m.
The probability of non-occurrence of A is given by P(\bar { A }) = 1 – P(A).

Addition Rule of Probabilities
If A and B are two events associated with a random experiment, then
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Similarly, for three events A, B, and C, we have
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(A ∩ C) – P(B ∩ C) + P(A ∩ B ∩ C)

Note: If A andB are mutually exclusive events, then
P(A ∪ B) = P(A) + P(B)

Android App

eVidyarthi

Search On eVidyarthi

Evidyarthi on Facebook

Like us on Facebook

Follow Evidyarthi on Youtube

Learn English
Learn English Through हिन्दी
Job Interview Skills
English Grammar
हिंदी व्याकरण - Vyakaran
Mathematics Class 6th
Science Class 6th
हिन्दी Class 6th
Mathematics Class 7th
Science Class 7th
हिन्दी Class 7th
हिन्दी Class 8th
Mathematics Class 8th
Mathematics Class 9th
English Class 9th
Science Class 9th
Mathematics Class 10th
English Class 10th
Mathematics Class XI
Chemistry Class XI
Accountancy Class 11th
Accountancy Class 12th
Mathematics Class 12th
Microsoft Word
Microsoft Excel
Microsoft PowerPoint
Adobe PhotoShop
Adobe Illustrator
Learn German
Learn French
IIT JEE
Privacy Policies, Contact Us
Copyright © 2020 eVidyarthi and its licensors. All Rights Reserved.