Theoretical Probability
Predicting outcomes using mathematics, not guesswork
The Probability Formula
Where:
- P(E) = Probability of event E
- n(E) = Number of favourable outcomes
- n(S) = Total number of possible outcomes
The Probability Scale
All probabilities fall between 0 and 1
The Complement Rule
The probability of an event NOT happening
Worked Example
Question:
A fair six-sided die is rolled. What is the probability of rolling an even number?
Solution:
Step 1: Sample Space S = {1, 2, 3, 4, 5, 6} → n(S) = 6
Step 2: Event E = {2, 4, 6} → n(E) = 3
Step 3: P(E) = 3/6 = 1/2 = 0.5 = 50%
Dice Roll Simulator
Click the die to roll it. Watch how the experimental probability of rolling an even number approaches 50%!
Theoretical probability of even number = 3/6 = 50%
Coin Flip Simulator
Click the coin to flip it. Watch how the experimental probability approaches 50% as you flip more!
Theoretical probability of heads = 1/2 = 50%
Card Probability Explorer
Click on cards to select them. The probability will update in real-time!
Spin the Probability Wheel
Click the wheel to spin! Each color represents a different outcome.
Test Your Knowledge
Question 1: A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?
Question 2: What is the probability of rolling a number greater than 2 on a standard die?
Question 3: If P(E) = 0.35, what is P(not E)?
