Probability is the study of chance. When studying probability, there are two very general classifications: ** theoretical probability **and

**.**

*experimental probability*-
is the calculated probability that a given outcome will occur if the same experiment were completed an infinite number of times.*Theoretical probability* -
is the observed result of an experiment conducted a limited number of times.*Experimental probability*

The probability of a simple event is the calculated chance of a specific direct outcome of a single experiment where in all possible outcomes are equally likely. To calculate the probability of such an outcome, we use a very simple and intuitive formula:

**Vocabulary**

An **event **is something that occurs, or happens, with one or more possible outcomes.

An **experiment **is the process of taking a measurement or making an observation.

A **simple event **is the simplest outcome of an experiment.

The **sample space **is the set of all possible outcomes of an experiment, typically denoted by \begin{align*}S\end{align*} .

To calculate the union, you just add up the individual probabilities of the events (**Additive Rule of Probability**).

*For mutually exlusive events:*

** conditional probability formula **:

\begin{align*}P(A|B)=\frac{P(A \cap B)}{P (B)}\end{align*}

This is read as "The probability that \begin{align*}A\end{align*} will occur, given that \begin{align*}B\end{align*} will occur (or has occurred), is equal to the intersection of probabilities \begin{align*}A\end{align*} and \begin{align*}B\end{align*} divided by the probability of \begin{align*}B\end{align*} alone".

**Complement of an Event**

The ** complement **of an event is the sample space of all outcomes that are

*not*the event in question.

Complements are notated using the prime symbol ’ as in: P(A') is the complement of P(A).

To calculate the probability of the complement of an event, use the following formula: P(A') = 1 - P(A)

Sometimes the probability of an event is difficult or impossible to calculate directly. In this case, it may be easier to caclulate the probability of the complement of the event, and then subtract that from 1 to get the probability of the actual event.