Question

If A and B are two events write the expression for the probability of occurrence of exactly one of two events.

Answer 1

$$\begin{gathered} P\left(\text{exactly one of 2 events}\right)=P\left(A\cup B\right)-P\left(A\cap B\right) \\ =P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)-P\left(A\cap B\right) \\ =P\left(A\right)+P\left(B\right)-2P\left(A\cap B\right) \end{gathered}$$