Venn Diagrams Flashcards
What is a Venn diagram?
It’s a box with circles in it. There are usually 2 or 3 overlapping circles, but there could be more or fewer.
How do you color the set A in this diagram?
Color in the whole circle with the name A.
How do you color the set B in this diagram?
Color in the whole circle with the name B.
How do you color the set A⋂B in this diagram?
- Lightly color in the set A.
- Lightly color in the set B.
- Erase anything that isn’t double colored.
How do you color the set A⋃B in this diagram?
- Lightly color in the set A.
- Lightly color in the set B.
- Everything that is colored is in A⋃B.
How do you color the set A’ (or Ac) in this diagram?
- Trace around the A circle.
- Lightly color everything that isn’t inside that circle.
What’s the first thing you should put in a Venn diagram?
The intersection!! If you haven’t been given the value for “both”, just put an x and calculate the rest as normal.
What does ⋃ mean when doing a Venn diagram?
Out loud it’s “or”, but it’s really “one or the other or both”…so…aaaanywhere in the two sets.
It’s officially called a “union,” and you can think of unions as welcoming places that bring everybody together. Anybody that is in any set of the union is welcome to be in the union.
What does ⋂ mean in a Venn diagram?
Out loud it’s “and”, so it’s only the stuff that’s in both sets at the same time.
It’s officially called an “intersection.” An intersection is a very exclusive place. The only things that are in the intersection are areas that are in all of the sets listed.
For example, this shaded region is A⋂B.
What does ‘ mean when doing Venn diagrams?
Out loud it’s “not”, so like “not A” or “not B”.
This figure represents C’ (read, “C prime”).
What do you do if it asks about something happening “given” something else happened already? So, the probability that somebody likes pineapple given that they like bananas.
This is “conditional probability” and you can either use a formula (in the IB booklets) or you can do it with your diagram.
- Color in the set that is “given”. This is your new universal set (the denominator).
- Find the number of observations in the intersection (“both”). This is the numerator.
For what types of problems should you use a Venn diagram (rather than a tree or a grid)?
For problems with a single event. Venn diagrams are used to describe a snapshot in time. It lets you visualize the relationship between different subgroups.
What does mutually exclusive mean?
When two events are mutually exclusive it is impossible for them to happen together:
- Turning left and turning right are mutually exclusive (you can’t do both at the same time)
- Tossing a coin: Heads and Tails are mutually exclusive (they can’t both happen at once)
- Cards: Kings and Aces are mutually exclusive (a card can only be one or the other)
How do mutually exclusive sets look in a Venn Diagram?
Circles that don’t overlap at all.
