Probability

Probability assigns a number between 0 and 1 to an event, representing how likely that event is to occur, where 0 means impossible and 1 means certain.

What is probability?

It’s the mathematical language for describing uncertainty: rather than saying an outcome simply “might” happen, probability lets you assign it a precise number, combine it with other probabilities, and reason formally about likely and unlikely outcomes.

Basic formula

For equally likely outcomes, P(event) = (number of favorable outcomes) / (total number of outcomes). More generally, probabilities must satisfy P(Ω) = 1 and be non-negative and additive over disjoint events.

Example

Rolling a fair six-sided die, the probability of rolling an even number is 3/6 = 1/2, since 3 of the 6 equally likely outcomes (2, 4, 6) are favorable.

Common mistakes

Confusing P(A and B) with P(A or B); treating dependent events as independent; forgetting that probabilities of an exhaustive set of outcomes must sum to 1.

Entropy

Questions about probability

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