Probability Fundamentals

Probability quantifies uncertainty. It is the mathematical language that underlies all of inferential statistics, from hypothesis testing to Bayesian reasoning. This lesson covers the core rules and concepts.

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What is Probability?

Probability is a number between 0 and 1 (or equivalently 0% and 100%) that describes the likelihood of an event occurring:

Probability	Interpretation
0	Impossible — the event cannot occur
0.5	Equally likely — a coin toss
1	Certain — the event must occur

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Key Terminology

Term	Definition
Experiment	A process that produces well-defined outcomes (e.g., rolling a die)
Sample space (S)	The set of all possible outcomes
Event (A)	A subset of the sample space — a specific outcome or set of outcomes
Complement (A')	All outcomes in S that are not in A

Example: Rolling a standard six-sided die

Sample space  S = {1, 2, 3, 4, 5, 6}
Event A       = "rolling an even number" = {2, 4, 6}
Complement A' = {1, 3, 5}

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