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.