SL 4.5—Probability basics

Probability starts with a defined sample space.

An event is a set of outcomes, and probabilities must be non-negative, sum to one across the sample space and reflect the stated model.

Example

For a fair die, P(even)=3/6=1/2 because the event {2,4,6} contains three equally likely outcomes.

Define the outcomes before using complements, unions or counting rules.

Equally likely is an assumption, not a property of every list of outcomes.

For equally likely outcomes in sample space $U$, $P(A)=n(A)/n(U)$ and $P(A')=1-P(A)$. Relative frequency estimates probability from observed trials. If an event has probability $p$ on each of $N$ comparable occasions, its expected number of occurrences is $Np$; for example, $128(0.1)=12.8$ means a long-run average, not that exactly 12.8 people can occur.