Events \(A\), \(B\), and \(C\) are defined on a probability space. Find expressions for the
following probabilities in terms of \(\mathbf{P}(A)\), \(\mathbf{P}(B)\), \(\mathbf{P}(C)\), \(\mathbf{P}(AB)\), \(\mathbf{P}(AC)\), \(\mathbf{P}(BC)\), and \(\mathbf{P}(ABC)\).
- The probability that exactly two of the \(A\), \(B\), \(C\) occur.
- The probability that exactly one of these events occurs.
- The probability that none of these events occur.
Here the notation \(AB\) is short for \(A \cap B\) which is the event “both \(A\) and \(B\)”
( [Pitman, p. 31, # 10])
