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LEARNING UNIT 5: Introduction to ProbabilityLearning objectives
• Understand and define different types of probabilities
• Describe properties of probabilities
• Apply rules of probabilities to solve problems
• Calculate probabilities from contingency tables and tree diagrams
• Use counting rules to count the number of outcomes in a sample or an event (not in 2021)
Textbook reference
Chapter 4
o §4.1 – §4.10
1
,INTRODUCTION
Inferential statistics is the branch of statistics that uses sample information to make estimates and
decisions concerning the entire population. Probability theory is used to assess how good such
estimates are in the face of uncertainty as it deals with the chance, likelihood or possibility that
an event may occur. The science of measuring uncertainty is called probability. It gives an
indication of how likely a particular outcome is and plays an important role in the decision making
process.
NOTATION AND TERMINOLOGY
Probability: A probability is between 0 and 1 inclusive, i.e. it cannot be negative and it cannot
exceed one.
Random experiment: A procedure that results in an uncertain outcome.
Sample space: The set of all possible outcomes of a random experiment, denoted by S. The
probability of the sample space is P S 1.
2
,Event: A subset or portion of the sample space. The probability of an event A is denoted by P A
Certain event: An event that is sure to occur. The probability of a certain event is 1.
Impossible event: An event that has no chance of occurring. The probability of an impossible
event is 0.
Empty set: A set that does not contain any of the outcomes of the sample space is called the empty
set, denoted by , and its probability is P 0 , i.e. the impossible event.
Elementary event: An event that has only one possible outcome.
The following concepts/terminology are illustrated using Venn diagrams. Venn diagrams are
used to visually represent events and how they co-exist in the sample space. The sample space is
represented by a rectangular box and circles are typically used to describe the events. The sizes
of the circles do not necessarily correspond to the sizes of the probabilities. Probability
calculations can become difficult using Venn diagrams. These diagrams are best used to visualise
events rather than to calculate probabilities of events. Other methods to represent probabilities
are discussed later in the unit.
3
, Complement of an event: The set of all outcomes of the sample space excluding the event itself.
Intersection of events: Intersection refers to where events occur together. The intersection of two
events A and B is denoted by A B and describes all the outcomes that are common to both A
and B, i.e. both A and B occurred.
4
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