Probability
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Cheat Sheets
Study MaterialProbability Cheat Sheet
Probability is one of the most important and scoring topics in Quantitative Aptitude and is frequently asked in SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand probability formulas, event concepts, conditional probability, coins, dice, cards, balls, and shortcut techniques for solving probability-based questions quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Probability for competitive exams:
Basic Concepts
- Probability Formula
- Favorable Outcomes
- Total Outcomes
- Range of Probability (0 to 1)
Types of Events
- Certain & Impossible Events
- Simple & Compound Events
- Independent & Dependent Events
- Mutually Exclusive Events
Addition Theorem
- P(A or B)
- Mutually Exclusive Events
- Non-Mutually Exclusive Events
- Intersection Concept
Multiplication Theorem
Probability of independent events occurring together.
Conditional Probability
- P(A|B)
- Dependent Events
- Conditional Outcomes
- Intersection Probability
Probability on Coins & Dice
- Head & Tail Problems
- Specific Number on Dice
- Sum & Product Problems
- Multiple Toss Problems
Cards & Balls Problems
- Deck of 52 Cards
- Face Cards & Suits
- Ball Selection Problems
- At Least One Event
Shortcut Tricks
Fast solving methods, complement probability tricks, and exam-oriented probability techniques.
Topics Covered
| Topic | Description |
|---|---|
| Probability Formula | Probability = Favorable Outcomes / Total Outcomes |
| Range of Probability | Probability value lies between 0 and 1 |
| Mutually Exclusive Events | Events that cannot occur together |
| Independent Events | Events not affecting each other |
| Dependent Events | Events affecting one another |
| Addition Theorem | Probability of occurrence of at least one event |
| Multiplication Theorem | Probability of simultaneous events |
| Conditional Probability | Probability under given condition |
| Coins Problems | Head-tail probability calculations |
| Dice Problems | Probability using six-faced dice |
| Cards Problems | Probability using deck of cards |
| Balls Problems | Selection probability from bags |
| At Least One Event | Complement probability concept |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand Probability Concepts
↓
Improve Logical Thinking
↓
Apply Shortcut Techniques
↓
Solve Probability Problems Faster
↓
Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Examples
Example 1:
Find the probability of getting a head when a coin is tossed once.
Total outcomes = 2
Favorable outcomes = 1
Probability = 1/2
Example 2:
Find the probability of getting number 4 on a die.
Total outcomes = 6
Favorable outcomes = 1
Probability = 1/6
Example 3:
A card is drawn from a deck of 52 cards. Find the probability of getting a king.
Number of kings = 4
Total cards = 52
Probability = 4/52
= 1/13
Example 4:
A bag contains 5 red and 3 blue balls. Find the probability of drawing a blue ball.
Total balls = 8
Blue balls = 3
Probability = 3/8
Example 5:
Two coins are tossed together. Find the probability of getting exactly one head.
Possible outcomes:
HH, HT, TH, TT
Favorable outcomes = HT, TH
Probability = 2/4
= 1/2
Final Takeaway
This Probability Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of event probability, conditional probability, cards and dice problems, and shortcut techniques can significantly improve speed, accuracy, and logical problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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