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  1. Basic Introduction

    Probability is the mathematics of uncertainty.

    AI/ML uses probability to:
    - predict outcomes
    - handle uncertain data
    - build models

2. Basic Terminology

Example:

3. Types of Events

Simple Event

Single outcome. Example:

Compound Event

Multiple outcomes. Example:

4. Probability Rules

Formula

Example:
Output:

5. Conditional Probability

Probability of A happening when B is true. Formula:
Example:

6. Law of Total Probability

Formula:
Example:

7. Bayes’ Theorem

Used heavily in ML classification. Formula:
Example:

8. Random Variable

A variable whose value depends on random outcomes. Types:
  • Discrete
  • Continuous
Example:

9. Mean, Median, Mode

Mean

Average value.
Example:

Median

Middle value.

Mode

Most frequent value.

10. Variance & Standard Deviation

Variance measures spread. Standard deviation is square root of variance. Example:

11. Probability Distributions

A probability distribution describes possible values and their probabilities. Types:
  • Bernoulli
  • Binomial
  • Uniform
  • Normal
  • Poisson

12. Bernoulli Distribution

Only two outcomes:
Example:

13. Binomial Distribution

Number of successes in repeated trials. Formula:
Example:

14. Uniform Distribution

All values have equal probability. Example:

15. Normal Distribution

Most common distribution in ML. Shape:
Example:

16. Poisson Distribution

Used for counting events. Examples:
  • website visits
  • failures
  • calls per hour
Formula:
Example:

AI/ML Probability Summary