section_path: Mathematical treatment/Mutually exclusive events
section_name: Mutually exclusive events
paragraph_text: Mutually exclusive events
  
  If either event A or event B can occur but never both simultaneously, then they are called mutually exclusive events.
  
  If two events are mutually exclusive, then the probability of both occurring is denoted as P (A ∩ B) {\displaystyle P(A\cap B)} and P (A and B) = P (A ∩ B) = 0 {\displaystyle P(A{\mbox{ and }}B)=P(A\cap B)=0} If two events are mutually exclusive, then the probability of either occurring is denoted as P (A ∪ B) {\displaystyle P(A\cup B)} and P (A or B) = P (A ∪ B) = P (A) + P (B) − P (A ∩ B) = P (A) + P (B) − 0 = P (A) + P (B) {\displaystyle P(A{\mbox{ or }}B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)=P(A)+P(B)-0=P(A)+P(B)}
  
  For example, the chance of rolling a 1 or 2 on a six-sided die is P (1 or 2) = P (1) + P (2) = 1 6 + 1 6 = 1 3. {\displaystyle P(1{\mbox{ or }}2)=P(1)+P(2)={\tfrac {1}{6}}+{\tfrac {1}{6}}={\tfrac {1}{3}}.}