Preliminary definitions

• Experiment ($\epsilon$): observation of a physical phenomenon. Of each REALIZATION or ESSAY of an experiment, an OUTCOME is obtained.
• Sample Space ($\Omega$): complete set of all the possible outcomes of an experiment.
• Event (A): set of outcomes of an experiment (a subset of the sample space).
• Certain event: An event which is sure to occur at every performance of an experiment is called a certain event connected with the experiment (‘head or tail’ is a certain event when tossing a coin).
• Impossible event: An event which cannot occur at any performance of the experiment is called an impossible event (`seven’ in case of throwing a die).
• Inclusion (or implication) ($A\subset B$). A is included in B (or A implies B) iff the occurrence of event A produces the occurrence of event B.
• Union of events A and B ($A\cup B$, or $A+B$): The union of events A and B holds true iff A or B holds true. It is not necessary that all events must hold true.
• Intersection (or product) ($A\cap B$, or $AB$): The intersection of events A and B can only be true iff both events hold true.
• Complementary event: An event B is complementary of A, if it is verified if and only if (iff) A is not verified (‘head’ and ‘tail’ are complementary to each other in the experiment of tossing a coin).
• Mutually Exclusive events (or incompatible): A and B are mutually exclusive iff they are not verified simultaneously (${\rm A}\cap {\rm B}=\varnothing$).
• Compound event: A is a compound event iff: