Probability – Types of Events

Probability – Types of Events

Event: An event is a subset of a sample space.

1. Simple event: An event containing only a single sample point is called an elementary or simple event.
2. Compound events: Events obtained by combining together two or more elementary events are known as the compound events or decomposable events.
3. Equally likely events: Events are equally likely if there is no reason for an event to occur in preference to any other event.
4. Mutually exclusive or disjoint events: Events are said to be mutually exclusive or disjoint or incompatible if the occurrence of any one of them prevents the occurrence of all the others.
5. Mutually non-exclusive events: The events which are not mutually exclusive are known as compatible events or mutually non exclusive events.
   
6. Independent events: Events are said to be independent if the happening (or non-happening) of one event is not affected by the happening (or non-happening) of others.
7. Dependent events: Two or more events are said to be dependent if the happening of one event affects (partially or totally) other event.

Mutually exclusive and exhaustive system of events:
Let S be the sample space associated with a random experiment. Let A₁, A₂, ……….. A_n be subsets of S such that
(i) A_i ∩ A_j = ϕ for i ≠ j and (ii) A₁ ∪ A₂ ∪ ….. ∪ A_n = S
Then the collection of events is said to form a mutually exclusive and exhaustive system of events.
If E₁, E₂, ……….. E_n are elementary events associated with a random experiment, then
(i) E_i ∩ E_j = ϕ for i ≠ j and (ii) E₁ ∪ E₂ ∪ ….. ∪ E_n = S
So, the collection of elementary events associated with a random experiment always form a system of mutually exclusive and exhaustive system of events.
In this system, P(A₁ ∪ A₂ ……… ∪ A_n) = P(A₁) + P(A₂) + …… + P(A_n) = 1