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# Compound Events

Let A and B be two events defined on a sample space S. We can combine A and B to form other new events which are called as compound events.

Some typical cases are:-

i.            A B is the event which occurs if both A and B occur.

ii.          A B is the event which occurs if either A or B or both occur.  In other words, A  B occurs if at least    one (of A, B) occurs.

# Mutually Exclusive Events

Two (or more) events are called mutually exclusive if they cannot occur simultaneously. Mathematically, if A and B are mutually exclusive, then

P (A  B) = 0

Illustration 4:

In throwing a fair die, event A occurrence of an odd number { 1, 3, 5) and event B occurrence of an even number {2, 4, 6) are mutually exclusive events because if odd number occurs, then even number cannot occur.

Also note that if events A and B are mutually exclusive, the compound event:

# Equally Likely Events

A number of sample events are said to be equally likely if there is no reason for one event to occur in preference to any other event.

#### Illustration 5:

When an unbiased die is thrown occurrence of numbers 1, 2, 3, 4, 5, 6 are equally likely.

# Exhaustive Events

If A1 , A2 ,.............An are events defined on a sample space S, and A1  A2  A3 ........  An = S, then these events are called as exhaustive events (i.e. one of these must occur).

# Complimentary Events

The event complimentary to A is a set of all those sample points of the sample space that are not present in set A. It is denoted by A. We can say that A occurs if A does not occur and vice-versa.

#### Illustration 6:

In throwing a fair die, events A {l, 3, 4, 6} and B {2, 5} are complimentary events because  ( there is no element common in set A and set B) and )