Classical Theoretical Probability
The theoretical probability of an event $E$, denoted by $P(E)$:
$$P(E) = \frac{\text{Number of outcomes favorable to } E}{\text{Total number of possible outcomes of the experiment}}$$
Axioms:
- $0 \le P(E) \le 1$
- $P(\text{Sure Event}) = 1$
- $P(\text{Impossible Event}) = 0$
- Complementary Event: $P(E) + P(\bar{E}) = 1 \implies P(\bar{E}) = 1 - P(E)$
Playing Cards Reference (52 Cards):
- 4 Suits of 13 cards each: Spades ($\spadesuit$, Black), Clubs ($\clubsuit$, Black), Hearts ($\heartsuit$, Red), Diamonds ($\diamondsuit$, Red).
- Face Cards (12): 4 Kings, 4 Queens, 4 Jacks.
- Aces (4): 1 per suit.
