This document introduces probability and key concepts in sets and events. It defines what a set is and how they can be described. It discusses subsets and Venn diagrams for visualizing relationships between sets. Operations on sets like union, intersection, difference and complement are covered. Random experiments and defining a sample space are introduced. Events can be mutually exclusive or collectively exhaustive over the sample space. Key probability concepts like mutually exclusive and exhaustive events are defined.

1. PROBABILITY
By:
1. Rana Sajjad Ali,
2. Abdullah Zafar,
3. CH. Faiq Shabbir,
4. Muhammad Rizwan,
5. Jawad

2. CONTENTS:
 Introduction to probability
 Sets
 Describing sets
 Subsets
 Venn Diagram
 Operations on sets
1. Union
2. Intersection
3. Difference
4. Complement
 Random Experiment
 Sample Space
 Events:
1. Mutually exclusive events
2. Exhaustive Events

3. INTRODUCTION:

4. Sets:
Set is a collection of distinct objects.
 A set is a gathering together into a
whole of definite, distinct objects of
our perception [Anschauung] or of
our thought—which are
called elements of the set.

5. Elements:
 Elements are the building blocks of the sets.

6. Describing a SET:
The Roster method:
A={1,3,5,7,9,11}
Descriptive method:
A={set of odd integers less than 13}
Set Builder Notation:
A={x|x is an odd Number x<12}

7. SUBSETS:
A is subset of B
A set that consists of some elements or
members of another set, is called a subset of
that set.
Here A is subset of B
Supersets:
Here B is
superset of A.

8. VEN DIAGRAM:

9. Operation on sets:
complementation
U
A
A-B
Difference

10. Random Experiment:

16. Mutually exclusive Events
HEAD
TAIL

18. Exhaustive Events:
Events are said to be collectively
exhaustive when the union of
mutually exclusive events is the
entire sample space S.