Topics
Goods and Services Tax (G.S.T.)
Commercial Mathematics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Banking
Algebra
Geometry
Shares and Dividends
Mensuration
Linear Inequations
Trigonometry
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Statistics
Ratio and Proportion
Probability
Factorisation of Polynomials
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic and Geometric Progression
Co-ordinate Geometry
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Symmetry
Similarity
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Circles
Tangent and Secant Properties
Constructions
Area and Volume of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Statistics : basic concepts, Mean, Median, Mode. Histograms and Ogive
Probability
Estimated time: 3 minutes
Maharashtra State Board: Class 10, 12
CISCE: Class 10
CISCE: Class 10
Key Points: Types of Events in Probability
| Type of Event | Meaning | Probability |
|---|---|---|
| Sure (Certain) Event | An event that is certain to occur | P(E) = 1 |
| Impossible Event | An event that cannot occur | P(E) = 0 |
| Simple (Elementary) Event | An event having only one outcome | P(E) = 1 / n(S) |
| Complementary Event (E̅) | An event that occurs when E does not occur | P(not E) = 1 − P(E) |
| Mutually Exclusive Events | Two events that cannot occur together | P(A ∩ B) = 0 |
| Exhaustive Events | Events which together cover all outcomes of S | P(A₁) + P(A₂) + … = 1 |
| Equally Likely Events | All outcomes have the same chance of occurring | P(E) = n(E) / n(S) |
| General Rule | Probability of any event | 0 ≤ P(E) ≤ 1 |
Properties:
- Complement Rule
P(A′) = 1 − P(A)
⇒ P(A) + P(A′) = 1 - Range of Probability
0 ≤ P(A) ≤ 1 - Impossible Event
P(ϕ) = 0 - Certain Event
P(S) = 1 - Subset Rule
If A ⊆ B, then P(A) ≤ P(B) - Difference of Events
P(A ∩ B′) = P(A) − P(A ∩ B)
P(A′ ∩ B) = P(B) − P(A ∩ B) - Union of Two Events
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) - Union of Three Events
P(A ∪ B ∪ C) = P(A) + P(B) + P(C)
− P(A ∩ B) − P(B ∩ C) − P(C ∩ A) + P(A ∩ B ∩ C) - Mutually Exclusive Events (2 events)
If A ∩ B = 0, then
P(A ∪ B) = P(A) + P(B) - Mutually Exclusive Events (multiple)
P(A₁ ∪ A₂ ∪ ... ∪ Aₙ) = P(A₁) + P(A₂) + ... + P(Aₙ) - Upper Bound of Union
P(A ∪ B) ≤ P(A) + P(B)
Video Tutorials
Shaalaa.com | Probability of the Complement of an Event
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