General competition

Probability Formulas

1. Probability

P(A) = favourable outcomes / total outcomes

👉 किसी घटना के होने की संभावना

🎲 Dice में 6 आने की probability = 1/6

2. Complement

P(A') = 1 - P(A)

👉 घटना A के न होने की संभावना

P(6) = 1/6 → P(not 6) = 5/6

3. Addition Rule

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

👉 जब दोनों events साथ हो सकते हैं

Mutually Exclusive: P(A ∪ B) = P(A) + P(B)

🪙 Head या Tail → 1/2 + 1/2 = 1

4. Multiplication Rule

P(A ∩ B) = P(A) × P(B|A)

👉 Dependent case

Independent: P(A ∩ B) = P(A) × P(B)

🪙🪙 Head & Head = 1/2 × 1/2 = 1/4

5. Conditional Probability

P(A|B) = P(A ∩ B) / P(B)

👉 B हो चुका है, अब A की probability

🎴 Red card में King = 1/13

6. Total Probability

P(A) = P(A|B)P(B) + P(A|B')P(B')

🏭 Different machines से total defect

7. Bayes Theorem

P(B|A) = [P(A|B) × P(B)] / P(A)

👉 Result से cause निकालना

🎯 Quick Revision

Mutually Exclusive = Add
Independent = Multiply
Conditional = Divide

📊 Probability Formulas