$$P(A) = \frac{\text{number of favourable outcomes}}{\text{total number of possible outcomes}} \qquad 0 \le P(A) \le 1$$ $$P(\text{not } A) = 1 - P(A) \qquad \text{sum of all probabilities} = 1$$

Combined events

• Independent events (AND): $P(A \text{ and } B) = P(A)\times P(B)$.
• Mutually exclusive events (OR): $P(A \text{ or } B) = P(A) + P(B)$.
• General OR: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
• Conditional (without replacement): $P(A \text{ then } B) = P(A)\times P(B \mid A)$.

Tree diagrams

Multiply along the branches, add the results of the different paths that give the required outcome.

Expected number

$$\text{Expected number of occurrences} = P(\text{event})\times\text{number of trials}$$