properties of probability

Basic properties:

For events A and B,

 i) P(A∪B) = P(A) + P(B) - P(A∩B)

 ii) P(A∩B) = P(A)P(B|A)

 iii) A and B as exclusive events ⇔ A∩B = Φ ⇔ P(A∩B) = 0

 iv) A and B as independence ⇔ P(A∩B) = P(A)P(B)