From weather patterns to the roll of a die. Master the objective measurement of likelihood and the laws of chance.
Probability is the measurement of the likelihood of events. While we can't always predict exactly what will happen (randomness), we can use data to express our confidence in an outcome.
Probability is always between 0 and 1.
A situation where you know all possible outcomes, but cannot predict which one will occur in a single trial.
Commonly called a 'trial'. An action like tossing a coin where the result is an outcome.
There are two primary ways to estimate probability objectively:
Based on relative frequency from past trials or data analysis.
Based on logic in an ideal, perfectly fair situation where all outcomes are equally likely.
Originated in ancient India as Jñān-Chaupad̤. It used dice to teach moral consequences (ladders = virtues, snakes = vices).
As the number of trials increases, the experimental probability tends to get closer and closer to the theoretical probability.
The misconception that if heads appears 6 times in a row, tails is "due". Reality: The coin has no memory. Each toss is independent.
To calculate probability accurately, we must define the boundaries of our experiment.
The set of all possible outcomes.
A specific subset of the sample space.
A tree diagram is a visual way to list all possible outcomes of a multi-step experiment, like tossing a coin twice.
Total outcomes: 4. Sum of probabilities: 1.0.