Chapter 14: Probability
Theoretical Probability, Complementary Events, and Deck of Cards Masterclass.
🎲 Theoretical Probability
Also called classical probability, formulated by Pierre Simon Laplace (1795).
The probability of any event P(E) always lies between 0 and 1 (inclusive): 0 ≤ P(E) ≤ 1.
🔄 Complementary Events
The event E (not E) represents the complement of event E.
• Probability of a sure event = 1.
• Probability of an impossible event = 0.
🃏 The 52 Playing Cards Anatomy
Standard deck of cards is divided equally into 4 suits of 13 cards each.
Hearts (♥): 13 cards
Diamonds (♦): 13 cards
Spades (♠): 13 cards
Clubs (♣): 13 cards
4 Kings, 4 Queens, 4 Jacks
(6 Red face cards, 6 Black face cards)
⭐ Board Exam Super-Hacks
Two Dice Sample Space Trick
When throwing two dice simultaneously, total possible outcomes = 6 × 6 = 36. For a sum of 8, look for pairs: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes → Probability = 5/36.
Sum of Elementary Probabilities
The sum of the probabilities of all the elementary events (events with a single outcome) of an experiment is always 1.
⚠️ Common Exam Traps
Trap 1: Probability Greater than 1
If your calculated probability is greater than 1 (e.g., 3/2) or negative (e.g., -1.5), your answer is mathematically wrong. Probability can NEVER exceed 1 or be negative!
Trap 2: Card Drawing Without Replacement
If a card/ball/pen is drawn and NOT replaced, remember to reduce the total number of outcomes (denominator) by 1 for the next draw (e.g., from 52 to 51 cards)!