Probability rules

Summary

If \(A\) and \(B\) are events and \(S\) is the sample space then we must have

• \(0≤P(A)≤1\)
• \(P(S)=1\)
• \(P(∅)=0\)
• If \(A\) and \(B\) are mutually exclusive then \(P(A∪B)=P(A)+P(B)\)
• \(P(A^C)=1-P(A)\)
• If \(B⊂A\) then \(P(B)≤P(A)\)
• \(P(A∪B)=P(A)+P(B)-P(A∩B)\) for arbitrary events \(A\) and \(B\)

Rule number 4 can be extended to an arbitrary number of events.