Algebra of Events
Two or more sets can be combined using four different operations, union, intersection, difference, and compliment. Since events are nothing but subsets of sample space, which means they are also set by themselves. In the same manner, two or more events can be combined using these operations. Let’s consider three events A, B, and C defined over the sample space S.
Complimentary Event
For every event A, there exists another event A’, which is called a complimentary event. It consists of all those elements which do not belong to event A. For example, in the coin-tossing experiment. Let’s say event A is defined as getting one head.
So, A = {HT, TH, HH}
The complementary A’ of event A will be consists of all the elements in the sample space which are not in event A. Thus,
A’ = {TT}
Event A or B
The Union of two sets A and B is denoted as A ∪ B. This contains all the elements which are in either set A, set B, or both. This event A or B is defined as,
Event A or B = A ∪ B
A ∪ B = {w : w ∈ A or w ∈ B}
Events A and B
The intersection of two sets A and B is denoted as A ∩ B. This contains all the elements which are in both set A and set B. This event A and B is defined as,
Event A and B = A ∩ B
A ∩ B= {w: w ∈ A and w ∈ B}
Event A but not B
The set difference A – B consists of all the elements which are in A but not in B. The events A but not B are defined as,
A but not B = A – B
A – B = A ∩ B’
Where B’ is the complement of event B.
Events in Probability
Events in Probability- In Probability, an event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space.
In this article, we will learn about the Events in Probability, Types of Events in Probability, definitions, how they are classified, how the algebra of events works, etc.
Table of Content
- Events in Probability
- Probability of Events
- Types of Events in Probability
- Union and Intersection of Events
- Algebra of Events
- How to Find the Probability of an Event
- Sample Problems on Events in Probability