Probability Formulas
🔢 Probability Formulas – 2-Page Cheat Sheet
| Basic Term | Formula | Memory Trick |
|---|---|---|
| Probability of an Event E | P(E) = (No. of favourable outcomes) / (Total possible outcomes) | F/T = Favourable ÷ Total |
| Range of Probability | 0 ≤ P(E) ≤ 1 | 0 = impossible, 1 = sure shot |
| Complement Rule | P(not E) = 1 – P(E) | “1 minus what you see” |
| Addition Rule (OR) | P(A ∪ B) = P(A) + P(B) – P(A ∩ B) | “Add, then subtract the overlap” |
| Mutually Exclusive | P(A ∪ B) = P(A) + P(B) | No overlap → no subtraction |
| Multiplication Rule (AND) | P(A ∩ B) = P(A) × P(B | A) |
| Independent Events | P(A ∩ B) = P(A) × P(B) | “No influence—just multiply straight” |
| Conditional Probability | P(B | A) = P(A ∩ B) / P(A) |
🎯 Quick-Fire Facts
- Impossible event → P = 0
- Sure event → P = 1
- Odds in favour = Favourable : Unfavourable
- At least one = 1 – P(none)
- Deck cards – 52 cards, 4 suits, 13 per suit, 26 red, 26 black
- Dice – 6 faces; sum of opposite faces is always 7
- Coin – 2 outcomes; P(H) = P(T) = ½
🧠 Mnemonics
- “1 – None = At-least-one” → always use for “at least one hit” questions
- “Add-Subtract-Overlap” → Addition rule reminder
- “Multiply-if-Independent” → no condition, straight multiply
📊 Comparison Table: Independent vs. Mutually Exclusive
| Feature | Independent | Mutually Exclusive |
|---|---|---|
| P(A ∩ B) | P(A)·P(B) | 0 |
| P(A ∪ B) | P(A)+P(B)–P(A)·P(B) | P(A)+P(B) |
| Example | Two separate coins | Heads & Tails on 1 coin |
⚡ Rapid-Fire MCQs
-
A card is drawn from a 52-deck. P(face card) = ?
a) 3/13 b) 4/13 c) 1/13 d) 12/52 -
Two coins tossed. P(at least one head) = ?
a) ¾ b) ½ c) ¼ d) 1 -
P(A)=0.3, P(B)=0.4, A & B independent. P(A ∩ B)=?
a) 0.7 b) 0.12 c) 0.58 d) 0.5 -
Rolling a die. P(prime number) = ?
a) ½ b) 1/3 c) 2/3 d) 4/6 -
P(E)=0.25. P(not E)=?
a) 0.75 b) 0.25 c) 1 d) 0 -
Two dice rolled. P(sum=7) = ?
a) 1/12 b) 1/6 c) 1/4 d) 5/36 -
Event with P=0 is called?
a) Sure b) Impossible c) Random d) Independent -
In a deck, P(red or king) = ?
a) 7/13 b) 1/2 c) 15/26 d) 28/52 -
If P(A∪B)=0.6, P(A)=0.3, P(B)=0.5, find P(A∩B).
a) 0.2 b) 0.3 c) 0.4 d) 0.1 -
A bag has 3 red, 2 blue. P(red) = ?
a) 3/5 b) 2/5 c) 1/5 d) 4/5
BETA
