Additive Probability Explained with Event Types and Practical Examples

Additive Probability Made Simple (With Real-Life Examples)

📚 Table of Contents

• Core Idea
• Additive Rule
• Event Types
• Marbles Example
• Cricket Example
• Dice Example
• Coin Example
• Zoo Example
• Code Example
• CLI Output
• Key Takeaways

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🧠 Core Idea

Additive probability helps us answer one simple question:

💡 “What is the chance that at least ONE of these events happens?”

For example: - Getting a 3 OR 4 in a dice - Picking red OR blue marble

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📐 Additive Rule

General Formula:

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

👉 Why subtract? Because sometimes events overlap, and we would count them twice.

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📍 Types of Events

1. Mutually Exclusive

Events that cannot happen together

2. Non-Mutually Exclusive

Events that can happen together

💡 Key difference:
- Exclusive → no overlap
- Non-exclusive → overlap exists

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🎯 Example 1: Marbles

5 marbles: Red, Blue, Green, Yellow, Black

Find: P(Red OR Blue)

P(Red) = 1/5
P(Blue) = 1/5

P(Red OR Blue) = 1/5 + 1/5 = 2/5

✔ Mutually exclusive → cannot pick both at once

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🏏 Example 2: Cricket Scores

Event A: Score > 200

Event B: Score > 250

If score > 250, it automatically means > 200

💡 So overlap exists → non-mutually exclusive

Result:

P(A OR B) = P(A)

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🎲 Example 3: Dice

Find P(3 OR 4)

P(3) = 1/6
P(4) = 1/6

Total = 2/6 = 1/3

✔ Mutually exclusive

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🪙 Example 4: Coin

Heads OR Tails

1/2 + 1/2 = 1

✔ One of them MUST happen

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🦁 Example 5: Zoo Animals

Select Lion OR Tiger

Cannot select both → mutually exclusive

P(Lion OR Tiger) = P(Lion) + P(Tiger)

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💻 Code Example

# Simple probability addition

P_A = 1/5
P_B = 1/5

result = P_A + P_B
print(result)

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🖥 CLI Output

0.4

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🎯 Key Takeaways

✔ Additive rule helps combine probabilities ✔ Subtract overlap when events are not exclusive ✔ Mutually exclusive → simple addition ✔ Non-mutually exclusive → subtract overlap

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📚 Related Articles

• Permutations and Combinations
• Machine Learning Examples
• Gradient Boosted Trees

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🚀 Final Thought

If you remember just one thing:

💡 “Add probabilities… but don’t double count overlap.”