Use the definition of probability to verify rules:
- (2.4)
\(\frac{n(S) - n(E)}{n(S)} = 1 - \frac{n(E)}{n(S)}\)
- (2.5)
\(E\) and \(F\) disjoint implies \(n(E \cup F) = n(E) + n(F)\). So, probability of \(E \cup F = \frac{n(E \cup F)}{n(S)} = \frac{n(E) + n(F)}{n(S)}\) and probability of \(E\) \(+\) probability of \(F\) \(=\) \(\frac{n(E)}{n(S)} + \frac{n(F)}{n(S)}\).
- (2.6)
\(E\) and \(F\) not disjoint implies \(n(E \cup F) = n(E) + n(F) − n(E \cap F)\). So, probability of \(E \cup F = \frac{n(E \cup F)}{n(S)} = \frac{n(E) + n(F) - n(E \cap F)}{n(S)}\) and probability of \(E\) \(+\) probability of \(F\) \(−\) probability of \(E \cap F = \frac{n(E)}{n(S)} + \frac{n(F)}{n(S)} − \frac{n(E \cap F)}{n(S)}\).