probability and venn diagrams€¦ · what is a venn diagram venn diagrams are illustrations used...
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Probability and Venn Diagrams
Coach Whitt
Probability and Venn Diagrams
�What can we say about probability?– It is a measure of likelihood, uncertainty,
possibility, …
– And it is a number, numeric measure, between 0 and 1.
�Simply put:– It is the chance that something will happen.
�For every event we can carefully assign a number which lies between 0 and 1 inclusive.
Experimental vs Theoretical
Probability� Experimental Probability
– Determined by observing the results of an experiment.
• Experimental probability = Number of event occurrences
Total number of trials
� Theoretical Probability– The likelihood in an event of what SHOULD happen.
• Theoretical probability = Number of favorable outcomes
Total number of outcomes
� Conditional Probability
– the probability that event B occurs given that event A has already occurred.
Probability Terms
� Compound Events– made up of two or more simple events.
• The probability that a flight will be on time and the luggage arrives is an example of a compound event.
� Dependent Events– 2 or more events whose outcomes affect each other.
The probability of occurrence of one event depends on the occurrence of the other.
� Independent Events– 2 or more events whose outcomes do not affect each
other.
Probability Terms
� Mutually Exclusive Events– 2 outcomes or evens are mutually exclusive when they
cannot both occur simultaneously.
� Mutually Inclusive Events– 2 outcomes or events are mutually inclusive when they
can both occur simultaneously.
� Outcome– The possible results after a number trials in an
experiment.
What is a Venn Diagram
What is a Venn Diagram
� Venn Diagrams are illustrations used in different branches of mathematics such as Set Theory or Probability.
� They show the mathematical or logical relationship between different groups of things (sets).
� A Venn Diagram shows all the possible logical relations between the sets.
Contents
� Who is credited with discovering Venn Diagrams
� What does a Venn Diagram look like
� How to use a Venn Diagram
Who created Venn Diagrams� Venn Diagrams are named after
John Venn, a British philosopher and mathematician who introduced these in 1881.
� John Venn used the diagrams to illustrate ideas used in logic.
� A stained glass window in Caius College, Cambridge, where he studied and spent most of his life, commemorates John Venn and represents a Venn Diagram.
What does a Venn Diagram look
like?� The simplest and most common Venn Diagram is made of a
rectangle and two circles that have an overlapping region.• See picture belowTerms –
•Sample Space or Universal Set
(Rectangle)
• Contains all things being
considered
• Represented by the red
rectangle
•Sets (Circles)
• Different groups of things
being considered
• The intersecting part of the
circles contains numbers that
can be found in both sets
Venn Diagram Terms
� Sample Space– A sample space for an experiment is the set of
ALL experimental outcomes.
� Set: – A set is a collection of distinct objects,
considered as an object in its own right– Example:
• A class of AQR students• NBA teams• Result of a football game for a team (win, lose, tie)• Outcomes of rolling a die ( 1, 2, 3, 4, 5, 6)
Terms
� Union
– “A union B” is the set of all elements that are in A, or B, or both.
A B∪
Terms
A B
A B∩
•Intersection
•“A intersect B” is the set of all
elements that are in both A and B. A B∩
Terms
� Complement of an event A: AC
– Includes ALL sample points that are not in a set.
Mostly Terrible Movies
How to Use a Venn Diagram
� Venn Diagrams can be used to show relationships between sets of information
� Each circle represents a set of information
Turtles
Ninjas
Ninja Turtles
• There can be more than 2 circles in a Venn Diagram
• The more circles (Sets) in a Diagram,
the more complicated it can be.