Probability
View Questions of Probability
Probability
Quantitative Aptitude - Probability
Study of chance: predicting how likely an event is to occur.
1. Basic Concept
\( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)
2. Types of Events
- Independent events: One doesn’t affect the other.
- Dependent events: Outcome affects next.
- Mutually exclusive: Only one can happen at a time.
3. Key Rules
- \( P(A') = 1 - P(A) \)
- If A and B are independent: \( P(A \cap B) = P(A) \cdot P(B) \)
- If A and B are mutually exclusive: \( P(A \cup B) = P(A) + P(B) \)
4. Examples
- Probability of drawing ace from a pack: \( P = \frac{4}{52} = \frac{1}{13} \)
- Probability of getting head on a coin toss: \( \frac{1}{2} \)
5. Tips for Exams
- Always list all outcomes for clarity.
- Check whether events are independent or mutually exclusive.
6. Mistakes to Avoid
- Counting overlapping outcomes multiple times.
- Confusing 'and' with 'or' scenarios.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations
Other Subjects
- Prestressed Concrete
- Fluid Mechanics
- Geotechnical Engineering
- Ground Improvement Techniques
- Groundwater Engineering
- Highway Engineering
- Hydraulics and Hydraulic Machines
- Hydrology
- Irrigation Engineering
- Open Channel Flow
- Pavement Design
- Estimation, Costing and Valuation
- Railway Engineering
- Soil Mechanics
- Strength of Materials
- Structural Analysis
- Surveying
- Traffic Engineering
- Transportation Engineering
- Wastewater Treatment
- Water Supply and Sanitation
- Contracts and Specifications
- Reasoning
- Engineering Mathematics
- Air Pollution and Control
- Bridge Engineering
- Building Materials and Construction
- Concrete Technology
- Construction Equipment
- Construction Planning and Management
- Quantitative Aptitude
- Dam Engineering
- Design of RCC Structures
- Design of Steel Structures
- Drainage Engineering
- Earthquake Engineering
- Engineering Geology
- Engineering Graphics
- Engineering Mechanics
- Environmental Engineering
- General Awareness / General Knowledge (GK)