Independent events - Events `A` and `B` are said to be independent if occurrences or non occurrence of one does not affect the probability of occurrence or non-occurrence of the other.

(i) Two people holding a normal dice and the other a coin, throw them once, then getting a `6` on normal dice and getting a head on the coin are the examples of events which are independent.

(ii) From a nurn containing `2R, 3G` and `4W` balls, a ball is drawn its colour is noted, the ball is replaced in the urn and another ball is drawn. Getting a red and a red ball on both the occasion are the examples of events which are independent.

(iii) Similar example can be given in playing cards 'getting an ace' and 'an ace' in two successive draws from a well shuffled pack of `52` cards when the first drawn card is replaced in the pack before the second is drawn. If it is not replaced the events become dependent or contingent.

Note : Dependent/Independent events come from two different experiments while mutually exclusive events come form the same experiment.

`text(Important Result :)`

If `E_1` and `E_2` areJndependent events, then
(i) `E_1` and `barE_2` are independent events.
(ii) `barE_1` and `E_2` are independent events.
(iii) `barE_1` and `barE_2` are independent events.

`text(Funda :)`

If `E_1, E_2,.........E_n` are independent events, then

`P(E_1 uu E_2 uu .........uu E_n : ) = 1 - p(E_1 uu E_2 uu ........uu E_n)'`
`= 1 - p(E_1'nnE_2'nn...........nnE_n')`
`= 1 - p(E_1').p(E_2')............p(E_n')`