AI Basics with AK
Season 03 - Introduction to Statistics
Episode 05 - Probability Fundamentals
Today, we unravel the basics of probability.
What is Probability?
Probability measures how likely an event is to happen.
Values between 0 (impossible) and 1 (certain).
Expressed often as fractions, decimals, or percentages.
Intuition: If you toss a fair coin, probability of Heads = 0.5.
Key Terms
| Term | Meaning |
|---|---|
| Sample Space (S) | Set of all possible outcomes |
| Event (E) | A subset of the sample space |
| Outcome | A single result from the sample space |
Probability of an Event
P(E) = Number of favorable outcomes / Total number of outcomes
Example: Probability of getting Heads when tossing a coin:
P(Heads) = 1/2 = 0.5
Probability Rules — The Basics
Rule 1: 0 ≤ P(E) ≤ 1
Rule 2: P(S) = 1 (Probability of entire sample space is 1)
Rule 3: P(E^c) = 1 - P(E) (Complement rule)
Complement Rule Example
If probability of rain tomorrow is 0.3, then probability of no rain is:
P(No Rain) = 1 - 0.3 = 0.7
Addition Rule for Mutually Exclusive Events
P(A ∪ B) = P(A) + P(B)
Example: Probability of rolling a 1 or 2 on a die:
P(1 or 2) = 1/6 + 1/6 = 2/6 = 1/3
Conditional Probability Introduction
Probability of event A given event B has occurred: P(A|B)
Formula:
P(A|B) = P(A ∩ B) / P(B)
Conditional Probability Example
If a card is red, probability it is a heart:
P(Heart) = 13/52
P(Red) = 26/52
So,
P(Heart | Red) = P(Heart ∩ Red) / P(Red) = (13/52) / (26/52) = 1/2
Thank You
Next episode, we dive into Probability Distributions — how probabilities spread over many outcomes, both discrete and continuous.
