A random experiment has a set S of all possible outcomes, called the **sample space**. An individual outcome is a **sample point**, and an **event** is a subset of S. - A **certain event** is the whole sample space S. - An **impossible event** is the empty event. - The **complement** X' is the event that X does not occur. Probability measures how likely an event is, from 0 (impossible) to 1 (certain). Classical probability When the outcomes in a finite sample space are equally likely, P(X)=(n(X))/(n(S)) Empirical probability If an experiment is repeated many times, the probability of X is estimated by the limiting relative frequency number of occurrences of Xnumber of trials. Geometrical probability P(X)=(measure of the favourable region)/(measure of the whole region) General rules 0 <= P(X) 1, P()=0, P(S)=1 P(X')=1-P(X), '=S, S'=

A random experiment has a set \(S\) of all possible outcomes, called the **sample space**. An individual outcome is a **sample point**, and an **event** is a subset of \(S\).

A **certain event** is the whole sample space \(S\).

An **impossible event** is the empty event \(\varnothing\).

The **complement** \(X'\) is the event that \(X\) does not occur.

Probability measures how likely an event is, from \(0\) (impossible) to \(1\) (certain).

When the outcomes in a finite sample space are equally likely,

Equally likely outcomes

If an experiment is repeated many times, the probability of \(X\) is estimated by the limiting relative frequency \(\dfrac{\text{number of occurrences of }X}{\text{number of trials}}\).

\[P(X)=\frac{\text{measure of the favourable region}}{\text{measure of the whole region}}\]

Probability Language and Basic Rules

Probability Language and Basic Rules