## Quick Reference

A subset of the sample space relating to an experiment. For example, suppose that the sample space for an experiment in which a coin is tossed three times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, and let *A*={HHH, HHT, HTH, THH}. Then *A* is the event in which at least two ‘heads’ are obtained. If, when the experiment is performed, the outcome is one that belongs to *A*, then *A* is said to have occurred. The intersection *A* ∩ *B* of two events is the event that can be described by saying that ‘both *A* and *B* occur’. The union *A* ∪ *B* of two events is the event that ‘either *A* or *B* occurs’. Taking the sample space as the universal set, the complement *A′* of *A* is the event that ‘*A* does not occur’. The probability Pr(*A*) of an event *A* is often of interest. The following laws hold:*A* ∪ B)=Pr(*A*)+Pr(*B*)−Pr(*A* ∩ *B*).*A* and *B* are mutually exclusive events, Pr(*A* ∪ *B*)=Pr(*A*)+Pr(*B*).*A* and *B* are independent events, Pr(*A* ∩ *B*)=Pr(*A*) Pr(*B*).*A′*)=1−Pr(*A*).

*A* ∪ B)=Pr(*A*)+Pr(*B*)−Pr(*A* ∩ *B*).

*A* and *B* are mutually exclusive events, Pr(*A* ∪ *B*)=Pr(*A*)+Pr(*B*).

*A* and *B* are independent events, Pr(*A* ∩ *B*)=Pr(*A*) Pr(*B*).

*A′*)=1−Pr(*A*).

*Subjects:*
Mathematics.