Probability : SGT

Probability

Introduction to Probability

Aspect	Explanation	Example
Chance	Likelihood of an event happening	Chance of rain today
Certain Event	An event that always happens	Sun rises in the east
Impossible Event	An event that can never happen	Getting 8 on a dice
Possible Event	An event that may or may not happen	Tossing a coin for head

Memory Tip:
Probability always lies between 0 and 1.

Exam Tip:
If probability = 0 → impossible.
If probability = 1 → certain.

Basic Concepts of Probability

Term	Meaning	Formula / Note
Experiment	Any action with known possible outcomes	e.g., tossing a coin
Outcome	Result of an experiment	e.g., Head or Tail
Sample Space	Set of all possible outcomes	S = {H, T}
Event	Subset of sample space	E = {H}

Formula	Description
P(E) = Number of favorable outcomes / Total outcomes	For equally likely outcomes

Memory Trick:
Probability = Favourable ÷ Total

Exam Tip:
Use this formula only when outcomes are equally likely.

Types of Events

Type	Definition	Example
Mutually Exclusive	Events that cannot occur together	Getting 2 or 5 on a dice
Complementary	Event and its opposite	Getting Head and not getting Head

Rule	Formula
Complementary Rule	P(A) + P(not A) = 1

Memory Tip:
Complement of an event is what is left when the event does not occur.

Exam Tip:
If P(A) = 0.3 then P(not A) = 0.7

Probability with Deck of Cards

Event	Probability
Drawing an Ace	4 / 52 = 1/13
Drawing a Red Card	26 / 52 = 1/2

Memory Tip:
Every standard deck has 52 cards → No Jokers!

Exam Tip:
Always cancel fractions after forming probability.

Applications of Probability

Area	Application
Weather	Rainfall forecasting
Sports	Winning prediction
Traffic	Accident chance analysis
Medicine	Diagnosis and treatment success
Business	Risk and profit analysis

Memory Box:
Probability helps in decision making under uncertainty.

Exam Tip:
Most application-based questions are scenario driven. Focus on identifying total outcomes first.