Page 3 - Xl-CH-16-LESSON NOTE

COMPLEMENTARY EVENT

Corresponding to every event an associated to a random experiment there exist an

event called complementary event to A. It is also called “not A” denoted by A′ or
MUTUALLY EXCLUSIVE EVENT:

The events and associated with an experiment said to be mutually exclusive iff
1
2
they do not occur simultaneously

i.e., iff ∩ = ∅
2
1
MUTUALLY EXCLUSIVE AND EXHAUSTIVE EVENTS :

Let S be a sample space associated with a random experiment. The events , ,…,

1
2
are said to be a form a set of manually exclusive and exhaustive system of events if
(i) ∪ …… ∪ = S i.e. , events , , ………. , are exhaustive events
1
2

1
2

(ii) ∩ = ∅ for i not equal j i.e. , events , , ………. , are mutually

1
2

exclusive , i.e. .., no two can occur simultaneously .
AXIOMATIC APPROACH TO PROBABILITY:
Let S be the sample space and E be an event.
(i) P(∅) = 0
(ii) P(S) = 1
(iii) 0≤ ( ) ≤ 1

Mathematical Definitation of probability:

Let S be the sample space and E be an event.

( )
P(E) = =
( )

Example :1 A coin is tossed two times. What is the probability of both are tail.

Ans : A coin is tossed two times.

S = {TT, TH, HT, HH} ⇒ ( ) = 4

E = Event of getting both are tail. ⇒ ( ) = 1