Self doubt

Question

What is the difference between Mutually exclusive event and independent event.??

Please explain, someone ASAP

Comments

$\bullet\; $Two events A and B are mutually exclusive ​​​​​​if

$P(A\cap B)=0\implies P(A\cup B)=P(A)+P(B)$

$P(A|B)=0$

$\bullet\;  $If events A and B are independent events then--  $P(A\cap B)=P(A)P(B)$

$P(A|B)=P(A|\neg B)=P(A)$

Answer 1

mutually exclusive means if A occurs then B does not occur. eg: like when we toss a coin , head and tail do not occur togather. i.e. P(A∩B)=0

independent events means B does not have any effect on outcome of A.  eg :-  tossing a coin does not have any effect on rolling a dice and getting 1 as outcome.

i.e. P(A|B)=P(A|¬B)=P(A)

eg :- P( rolling a dice and getting 1 as outcome/ given that you get a head) = P( rolling a dice and getting 1 as outcome ) = 1/6.