An Introduction to Venn Diagrams Slideshow 55,
MathematicsSlideshow 55, Mathematics Mr Richard Sasaki, Room 307Mr
Richard Sasaki, Room 307
Slide 2
Objectives Learn and review some new notation about different
events Learn and review some new notation about different events
Learn how Venn diagrams hold information Learn how Venn diagrams
hold information Understand how to calculate probabilities with
Venn diagrams Understand how to calculate probabilities with Venn
diagrams
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Notation At times, different events successes have
probabilities given to you. For an event A, we assume that A can
happen How do we write the probability of event A? P(A) How do we
write the probability of event B? P(B) How do we write the
probability of event A and B? A or not happen! A
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Venn Diagram A Venn Diagram is a diagram that shows relations
between sets. Set A Set B But what if values in Set A could also be
in Set B?
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Venn Diagram Lets make a Venn diagram about you! I want you to
think about something tasty. Which do you prefer, chocolate or
biscuits? Or both? Or neither?! Which is Set A? Which is Set B? Set
A Set B Complete the first three rows of the table.
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Complements How do we write the probability of picking
something that isnt in Set A? P(A') P(A') = 1 P(A) Example P(A')
=
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Answers Question 1 3227 39 2 Set ASet B Question 2 2 7 41 0 Set
ASet B
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Practice Lets have a bit of practice to make sure that everyone
is going in the right direction. Example Draw a Venn diagram
representing a sample of 100 people where 79 people like sushi (Set
A), 68 people like sashimi (Set B) and 48 people like both. What is
the area shown? Set A but not B Set A and B Set ASet B Set B but
not A Neither Set A nor B
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Practice 4831 20 1 Set ASet B Note: The numbers should add up
to 100 (the sample size). If an element is picked at random,
calculate:
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Answers - Easy 5 14 8 3 Set ASet B 13 2 23
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Answers - Hard 26 96 42 36 Set ASet B 18 27 7 48 26 18
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Null Sets and Universal Sets You had to answer two questions
where you didnt know the notation (I assume). The empty set with a
probability of 0, we call the null set. This is denoted (phi). The
set that includes everything, with a probability of 1 is the
universal set. Ironically, its not very universal and goes by many
symbols. I used (omega) which is one of the more common ones.
