This module provides a review of the probability formulas, including the definitions of independent, complementary, and mutually exclusive events as well as the addition and multiplication rules.
Formula
Complement
If
$A$ and
$\mathrm{A\text{'}}$ are complements then
$\mathrm{P(A)}+\text{P(A' )}=1$
Formula
Addition rule
$\text{P(A OR B)}=\text{P(A)}+\text{P(B)}\text{P(A AND B)}$
Formula
Mutually exclusive
If
$A$ and
$B$ are mutually exclusive then
$\text{P(A AND B)}=0$ ; so
$\text{P(A OR B)}=\text{P(A)}+\text{P(B)}$ .
Formula
Multiplication rule

$\text{P(A AND B)}=\text{P(B)}\text{P(AB)}$

$\text{P(A AND B)}=\text{P(A)}\text{P(BA)}$
Formula
Independence
If
$A$ and
$B$ are independent then:

$\text{P(AB)}=\text{P(A)}$

$\text{P(BA)}=\text{P(B)}$

$\text{P(A AND B)}=\text{P(A)}\text{P(B)}$
Glossary
Conditional probability
The likelihood that an event will occur given that another event has already occurred.
Contingency table
The method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other. The table provides an easy way to calculate conditional probabilities
Equally likely
Each outcome of an experiment has the same probability.
Event
A subset in the set of all outcomes of an experiment. The set of all outcomes of an experiment is called a sample space and denoted usually by S. An event is any arbitrary subset in S. It can contain one outcome, two outcomes, no outcomes (empty subset), the entire sample space, etc. Standard notations for events are capital letters such as A, B, C, etc.
Experiment
A planned activity carried out under controlled condition.
Independent event
The occurrence of one event has no effect on the probability of the occurrence of any other event. Events A and B are independent if one of the following is true:
(1). P (A  B) = P (A)
(2). P (B  A) = P (B)
(3). P (A and B) = P (A) P(B)
Mutually exclusive
An observation cannot fall into more than one class (category). Being in more than one category prevents being in a mutually exclusive category.
Outcome
A particular result of an experiment.
Probability
A number between 0 and 1, inclusive, that gives the likelihood that a specific event will occur. The foundation of statistics is given by the following 3 axioms (by A. N. Kolmogorov, 1930’s): Let S denote the sample space and A and B are two events in S . Then:
(1). 0≤P(A)≤1
(2). If A and B are any two mutually exclusive events, then P(A or B)= P(A)+P(B)
(3). P(S)=1
Sample space
The set of all possible outcomes of an experiment.
Tree diagram
The useful visual representation of a sample space and events in the form of a “tree” with branches marked by possible outcomes simultaneously with associated probabilities (frequencies, relative frequencies).
Venn diagram
The visual representation of a sample space and events in the form of circles or ovals showing their intersection.