Different Types of Events in Probability

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 is an important topic for the JEE exam. 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 of E].

What are Different Types Of Events?

1. 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.

2. Impossible Event: If the probability of occurrence of an event is zero, then it is an impossible event. For example, getting 7 when a die is tossed.

3. Independent Events: When the outcome of the first event does not influence the outcome of the second event, those events are known as independent events. For example, choosing a marble from a bag and getting a tail after tossing a coin.

4. Dependent Events: When the outcome of the first event influences the outcome of the second event, those events are called dependent events. For example, if we draw two coloured marbles from a bag and the first marble is not replaced before you draw the second marble, then the outcome of the second draw will depend on the outcome of the first draw.

5. Mutually Exclusive Events: These events cannot happen at the same time. For example, while tossing a coin, head and tail are mutually exclusive. They cannot occur at the same time.

6. Complementary Event: For any event A, there exists another event A‘ which shows the remaining elements of the sample space S. A’ = S-A.

7. Compound Event: If an event has more than one sample point, it is termed as a compound event. For example, If S = {1,2,3,4,5,6} . E1 = {1,3,6} E2 = { 2,6}, E1 and E2 represents compound events.

8. Exhaustive Events: The events E1, E2 ,……., En are exclusive if E1⋃E2⋃…….⋃En = S, where S is the sample space.

9. Simple event: An event that has a single point of the sample space is known as a simple event in probability. For example, if S = {1,2,3,4} and E = {3} then E is a simple event.