Indepedent vs. Dependent events, Complements

Independent events
Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. This rule applies if and only if:

P(A│B)=P(A),
P(B│A)=P(B)
P(AB) = P(A│B) x P(B) = P(A) x P(B)

Notes:

• Two events are not independent when the conditional probability of A given B is higher or lower than the unconditional probability of A.

Dependent events
If the result of one event is affected by the result of another event, the events are said to be dependent.

Complements
The set of events are mutually exclusive and exhaustive. The complement of an event A is the set of all outcomes that do not include event A.

P(A)+P(A^c)=1
P(A^c│B)=P(A│B)=1