Another name for the mean of a probability distribution is expected value.

If $A$ and $B^{\prime}$ are independent events, then $P\left(A^{\prime} \cup B\right)=1-P(A) P\left(B^{\prime}\right)$.

If A and B are independent, then P (exactly one of $\mathrm{A}, \mathrm{B}$ occurs)

$$=P(A) P\left(B^{\prime}\right)+P(B) P\left(A^{\prime}\right) \text {. }$$

If $A$ and $B$ are two events such that $P(A)>0$ and $P(A)+P(B)>1$, then $P(B / A) \geq 1-\frac{P\left(B^{\prime}\right)}{P(A)}$

If $A, B$ and $C$ are three independent events such that

$$P(A)=P(B)=P(C)=p,$$

then $P$ (atleast two of $A, B$ and $C$ occur) $=3 p^2-2 p^3$.