1. Mutually exclusive events: Suppose, U is a finite sample space. A and B are any two events of U. If A ∩ B = Φ, then A and B are mutually exclusive events.
2. Union of events: Suppose, U is a finite sample space. A and B are any two events of U. Event A occurs or event B occurs or events A and B occur togethers, i.e., at least one of the events A and B occurs is called the union of events A and B. It is denoted by A ∪ B.
Thus, A ∪ B = {x; x ∈ A or x ∈ B or x ∈ A ∩ B}
3. Intersection of Events: Suppose, U is a finite sample space. A and B are any two events of U. The event that A and B occur together is called the intersection of events A and B. It is denoted by A ∩ B.
Thus, A ∩ B = {x; x ∈ A and x ∈ B}
4. Difference event: Suppose, U is a finite sample space. A and B are any two events of U. The event that A occurs but B does not occur is called the difference event of A and B. It is denoted by A – B or A ∩ B’. Similary, the event that A does not occur but B occurs is called the difference event of B and A. It is denoted by B – A or A’ ∩ B.
Thus, A – B = {x; x ∈ A and x ∉ B}
B – A = {x; x ∈ B and x ∉ A}
5. Exhaustive events: Suppose, U is a finite sample space. A and B are any two events of U. If A ∪ B = U, then A and B are called exhaustive events.
6. Complementary event: Suppose, A is any event of the finite sample space U. The event that A does not occur means the event consists of elements in U but not in A is called the complementary event of A. It is denoted by A’. Thus,
A’ = {x; x ∉ A, x ∈ U}
