PROBABILITY - 2
Algebra of events ➖
Complementary event :-
It is a LEFTOVER PART OF THE event. Events mean what will happen.
~E = 1 - E
P(~E) - P(E) = 1
Event “ E1 and E2 “
It means the intersection of two events. And talking about common parts between them.
Event “ E1 or E2 “
It means the combination of two events. And talking about both together .
E1+E2
Event “ E1 But not E2 “
It means that all the E1 part will be present except the E2 part which means we have removed the common part from E1.
Event “neither E1 nor E2 “
All the outcomes which are not present in the E1 and E2.
ADDITION THEOREM ON PROBABILITY.
P( E1 union E2 )
Types of Events
Independent events
Dependent events
Two or more events are said to be independent if occurrence or non-occurrence of one event will not affect the probability of occurrence and non-occurrence of other event, then we will say events are independent otherwise events are said to be dependent.
Independent :-
P ( A / B ) = P ( A )
P ( B / A ) = P ( B )
( X / Y it mean that what is the probability X if Y has already happened )
Suppose three events A,B,C are independent then.
The probability of any one will not affect its future outcome.
But there are some more conditions that must be pairwise independent and mutually exclusive to each other.
Dependent :-
P ( A / B ) ! = P ( A )
P ( B / A ) != P ( B )
( != is not equal to )
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