Any subset of the sample space of a random experiment is called an event. It is denoted by letters A, B, C,…

1. Impossible Event:

• A special subset 0 or { } of the sample space U of any random experiment is called an impossible event.
• For example, an event of getting both H and T in a single toss of an unbiased coin is an impossible event.

2. Certain Event:

• A special subset U of the sample space U of any random experiment is called a certain event.
• For example, an event of getting H or T in a single toss of an unbiased coin is a certain event.

3. Intersection of two events A and B: If A and B be any two events of the finite sample space U, then the event that ‘event A and event B both occur simultaneously’ is called the intersection of events A and B. It is denoted by the symbol A ∩ B.
Thus, A ∩ B = {x; x ∈ A and x ∈ B}

4. Union of two events A and B: If A and B be any two events of the finite sample space U, then the event that ‘either event A or B or both occur together is called the union of two events A and B. It is denoted by the symbol A ∪ B. Thus, A ∪ B = {x; x ∈ A or x ∈ B or x ∈ A ∩ B}

5. Complementary Event: If A be an event of the finite sample space U, then, the event that A does not occur is defined as the set of those elements (or outcomes) of sample space U, which are not in A is called the complementary event of A. It is denoted by the symbol A’, A̅ or Ac.
Thus, A’ = {x; x ∉ A, x ∉ U}

6. Mutually Exclusive Events: If A and B be any two events of a finite sample space; U, then the event that ‘events A and B; cannot occur together, i.e., if A ∩ B = Φ, the events A and B are said to be mutually exclusive events.

7. Difference Events: If A and B be any: two events of the finite sample space U, then the set of all those elements of U, which belong to event A but do not belong to event B is called the difference event of A and B. It is denoted by the symbol A – B or A ∩ B’. Similarly, the set of all those elements of U which belong to event B but do not belong to event A is called the difference event of B and A. It is denoted by the symbol B – A or B ∩ A’.
Thus, A – B = {x; x ∈ A and x ∉ B}
B – A = {x; x ∈ B and x ∉ A}

8. Exhaustive Events: If U is a sample space and A and B are any two events and A ∪ B = U, then events A and B are said to be exhaustive events.

9. Mutually Exclusive and Exhaustive Events: If A and B be any two events of a finite sample space U such that A ∪ B = U and A ∩ B = Φ then A and B are said to be mutually exclusive and exhaustive events.

10. Elementary Events: The events consisting of only a single element of a sample space U are called elementary events. The elementary events are mutually exclusive and exhaustive events.

11. Equi-probable Events: If there is no apparent reason to believe that out of one or more events of a random experiment, any one event is more or less likely to occur them the other events, then the events are called equi-probable events.

12. Favourable Outcomes:

If some elementary outcomes out of all the elementary outcomes of a random experiment indicate the occurence of an event A, then these outcomes are said to be favourable to the occurence of the event A.