Probability Formulas

🔢 Probability Formulas – 2-Page Cheat Sheet

🎯 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

⚡ Rapid-Fire MCQs

1. A card is drawn from a 52-deck. P(face card) = ?
   a) 3/13 b) 4/13 c) 1/13 d) 12/52

2. Two coins tossed. P(at least one head) = ?
   a) ¾ b) ½ c) ¼ d) 1

3. 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

4. Rolling a die. P(prime number) = ?
   a) ½ b) 1/3 c) 2/3 d) 4/6

5. P(E)=0.25. P(not E)=?
   a) 0.75 b) 0.25 c) 1 d) 0

6. Two dice rolled. P(sum=7) = ?
   a) 1/12 b) 1/6 c) 1/4 d) 5/36

7. Event with P=0 is called?
   a) Sure b) Impossible c) Random d) Independent

8. In a deck, P(red or king) = ?
   a) 7/13 b) 1/2 c) 15/26 d) 28/52

9. 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

10. A bag has 3 red, 2 blue. P(red) = ?
    a) 3/5 b) 2/5 c) 1/5 d) 4/5