Question

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

Answer 1

\[P\left( \text{ exactly one of 2 events } \right) = P\left( A \cup B \right) - P\left( A \cap B \right)\]
\[ = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right) - P\left( A \cap B \right)\]
\[ = P\left( A \right) + P\left( B \right) - 2P\left( A \cap B \right)\]