Non mutually exclusive events can occur jointly.
Example: In a deck of 52 cards, there are 4 suites (heart, diamond, club, spade), each suite has 4 face cards (ace, king, queen, jack) and 9 number cards (2-10). If event A is the card drawn is heart and event B is ace, these events can occur jointly as ace of hearts. Adding P(ace) + P(heart), we get = 4/52 + 13/52 = 17/52, but we know there are only 16 cards (13 hearts and 3 more aces). So that P(A and B) is not double counted , it must be subtracted from P(A) + P(B).
Generation Addition Rule: P(A or B) = P(A) + P(B) - P(A and B).
Applying the General Addition Rule to the example, P(ace or hearts) = 13/52 + 4/52 - 1/52 = 16/32
Select One:
General Multiplication Rule: P(A and B) = P(A) x P(B I A)
General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B)
Simple Addition Rule: P(A or B) = P(A) + P(B)
Simple Multiplication Rule: P(A and B) = P(A)*P(B)