## Probability – Types of Events

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

**Simple event:**An event containing only a single sample point is called an elementary or simple event.**Compound events:**Events obtained by combining together two or more elementary events are known as the compound events or decomposable events.**Equally likely events:**Events are equally likely if there is no reason for an event to occur in preference to any other event.**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.**Mutually non-exclusive events:**The events which are not mutually exclusive are known as compatible events or mutually non exclusive events.

**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.**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 A_{1}, A_{2}, ……….. A_{n} be subsets of S such that

(i) A_{i} ∩ A_{j} = *ϕ* for i ≠ j and (ii) A_{1} ∪ A_{2} ∪ ….. ∪ A_{n} = S

Then the collection of events is said to form a mutually exclusive and exhaustive system of events.

If E_{1}, E_{2}, ……….. E_{n} are elementary events associated with a random experiment, then

(i) E_{i} ∩ E_{j} = *ϕ* for i ≠ j and (ii) E_{1} ∪ E_{2} ∪ ….. ∪ 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(A_{1} ∪ A_{2} ……… ∪ A_{n}) = P(A_{1}) + P(A_{2}) + …… + P(A_{n}) = 1