operations with events

If we have two events, A and B, of the same sample space E:

–A is included in B, ACB, if every outcome of A is an outcome of B.

–The union event AUB is the event that happens when either A or B occurs.

–The intersection event A∩B is the event that happens when both A and B occur. These events are incompatible if A ∩B = ф

–The complement of event A,

, is the event that happens when A doesn’t ocur

Properties:

Exercise: if we roll a dice, let the events: A = {even}, B = {lower that 3}, c = {1,6}. Find the events:

a) AUB

b) A∩B

c) (A∩B)UC

d) Complement event of B

e) (AUB)∩C

f) A∩B∩C

Solutions: a) {1,2,4,6}; b) {2}; c) {1,2,6}; d) {3,4,5,6}; e) C = {1,6} f) Φ