Two events are said to be an event if happening of one event doesn't affect the other one.
let two event A and B are independent events then:
P(A ∩ B) = P(A). P(B)
from conditional probability theorem, we already know that
P(A/B)= P(A ∩ B) / P(B) .....................(1)
Since Events are independent then P(E/F)= P(E)
therefore P(A/B)= P(A) because happening of A is not depending on happening of B , they are Independent to each other.
Replacing P(A/B) with P(A) in equation (1)
P(A) . P(B) = P(A ∩ B)
for any number of events if this definition holds we can say that they are Independent events.
Please remember one thing Independent events are not Mutually exclusive events because In mutually exclusive events, A ∩ B = Ø
So P(A ∩ B ) = 0