🎲 Probability - Formula Sheet

🎯 Basic Probability

Simple Probability

P(Event) = (Number of Favorable Outcomes) / (Total Number of Outcomes)

Complement Rule

P(Event') = 1 - P(Event)
P(Not A) = 1 - P(A)

📊 Combined Probability

Addition Rule

P(A or B) = P(A) + P(B) - P(A and B)

Mutually Exclusive Events

P(A or B) = P(A) + P(B)  (when A and B cannot occur together)

Multiplication Rule

P(A and B) = P(A) × P(B|A)

Independent Events

P(A and B) = P(A) × P(B)  (when A doesn't affect B)

🔢 Special Cases

Conditional Probability

P(A|B) = P(A and B) / P(B)

Odds in Favor

Odds in favor = Favorable : Unfavorable
Probability = Favorable / (Favorable + Unfavorable)

Odds Against

Odds against = Unfavorable : Favorable
Probability = Favorable / (Favorable + Unfavorable)

🎲 Dice Problems

Single Die

Total outcomes = 6
P(even) = 3/6 = 1/2
P(prime) = 3/6 = 1/2

Two Dice

Total outcomes = 36
Sum of 7: 6 ways → P = 6/36 = 1/6
Double numbers: 6 ways → P = 6/36 = 1/6

🃏 Cards Problems

Standard Deck

Total cards = 52
Suits: 13 each (♥♦♣♠)
Face cards: 12 (J, Q, K)
Ace cards: 4

Common Probabilities

P(Heart) = 13/52 = 1/4
P(Face card) = 12/52 = 3/13
P(Ace) = 4/52 = 1/13

📝 Problem Types

With Replacement

P = P(Event₁) × P(Event₂) × ...
(Items returned to pool)

Without Replacement

P = P(Event₁) × P(Event₂|Event₁) × ...
(Items not returned)

At Least One

P(at least one) = 1 - P(none)

⚡ Quick Tips

1. Identify total outcomes first
2. Count favorable outcomes carefully
3. Check for replacement vs without replacement
4. Use complement for “at least one” problems
5. Remember: 0 ≤ P ≤ 1

Master Probability - Count carefully, think logically! 🎲