In Probability, we come across different types of events. The collection of some outcomes of an experiment is called an event. Probability comes into application in various fields. Probability refers to the occurrence of a random event. The probability of an event E is defined as P(E) = [Number of favourable outcomes of E]/[Total number of possible outcomes]. Probability is an important topic for the JEE exam. In this article, you will understand various types of events in probability with the help of examples.
What Are the Different Types of Events?
The different types of events in probability are:
- Sure event
- Impossible event
- Independent event
- Dependent event
- Mutually exclusive event
- Complementary event
- Compound event
- Exhaustive event
- Simple event
All these types of events are explained below with the help of examples.
Sure Event
It is an event that always occurs when an experiment is conducted. For example, getting a tail when a coin is tossed. The probability of a sure event is 1.
Example:
The probability of an event that has all outcomes of the experiment, i.e., sample space, is 1.
Impossible Event
If the probability of occurrence of an event is zero, then it is an impossible event.
Example: The event of getting 7 when a die is thrown is impossible. This is because the outcomes of throwing a die include {1, 2, 3, 4, 5, 6}.
Independent Event
When the outcome of the first event does not influence the outcome of the second event, those events are known as independent events.
Example: The event of getting a tail after tossing a coin and the event of getting a head when tossing another coin.
Dependent Event
When the outcome of the first event influences the outcome of the second event, those events are called dependent events.
Example: If we draw two coloured marbles from a bag and the first marble is not replaced before we draw the second marble, then the outcome of the second draw will depend on the outcome of the first draw.
Mutually Exclusive Event
These events cannot happen at the same time. They cannot occur at the same time.
Example: The events of getting head and tail are mutually exclusive while tossing a coin.
Complementary Event
For any event A, another event, A‘, shows the remaining elements of the sample space S. A’ = S – A.
Example: Suppose the set of the first 10 natural numbers is a sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A be the event of choosing an even number less than 10. So, A = {2, 4, 6, 8}
Thus, A’ = S – A = {1, 3, 5, 7, 9, 10}
Compound Event
If an event has more than one sample point, it is termed as a compound event.
Example: If S = {1, 2, 3, 4, 5, 6} such that E1 = {1, 3, 6}, E2 = {2, 6}. Thus, E1 and E2 represents compound events.
Exhaustive Event
The events E1, E2,……., En are exclusive if E1 ⋃ E2 ⋃…….⋃ En = S, where S is the sample space.
Example: Suppose E1 be the event of getting an even number and E2 be the event of getting an odd number when throwing a die.
Here, E1 = {2, 4, 6}, E2 = {1, 3, 5}
E1 ⋃ E2 = {1, 2, 3, 4, 5, 6} = S (sample space}
Thus, E1 and E2 are exhaustive events.
Simple event
An event that has a single point of the sample space is known as a simple event in probability.
Example: If S = {1, 2, 3, 4} and E = {3} then E is a simple event.
Recommended Videos
Probability of Independent Events – Solved Question
Mutually Exclusive Events – JEE Concept Video
Frequently Asked Questions
What are Compound Events?
If an event has more than one sample point, it is termed a compound event.
What are Mutually Exclusive Events?
Mutually Exclusive Events are events that cannot happen at the same time.
What do you mean by a Simple Event?
A Simple Event is an event where one experiment happens at a time and has a single outcome.
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