Probability Fundamentals

Introduction

Probability is a fundamental concept in data science and machine learning, serving as the backbone for statistical inference and decision-making under uncertainty. This lesson covers the essential concepts, definitions, and rules of probability.

Key Concepts

• Random Experiment
• Sample Space
• Event
• Probability of an Event
• Conditional Probability
• Independence

Definitions

Basic Rules of Probability

1. Rule of Addition: For any two events A and B,
   P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
2. Rule of Multiplication: For any two independent events A and B,
   P(A ∩ B) = P(A) * P(B)
3. Complement Rule: The probability of an event not occurring,
   P(A') = 1 - P(A)

Code Examples

Below is a simple Python example demonstrating basic probability calculations:

import random

# Function to simulate a random experiment
def simulate_experiment(trials):
    success_count = 0
    for _ in range(trials):
        outcome = random.choice(['H', 'T'])  # Heads or Tails
        if outcome == 'H':
            success_count += 1
    return success_count / trials

# Run the experiment
probability_of_heads = simulate_experiment(10000)
print(f"Estimated Probability of Heads: {probability_of_heads:.4f}")
                

FAQ