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Lets talk about
Definition:
A set is a collection of objects named elements.
Notation:
A set can be defined by listing its elements between
braces. Example: A = {1, 2, 3, 4, 5}.


If something is an element of a set we use .
If something is not an element we use .
Example: , .
A
89
A
2 

Lets talk about
If a set has no elements it is called the empty
set. It is written as ∅.
The universal set is the set of all elements
being considered. It is written 𝜉.
Lets talk about
The union of two sets, A and B, is the elements
in A or B or in both. It is written A ∪ B.

The intersection of two sets, A and B, is the
elements that are in A and B. It is written A ∩ B.
Example 1
A = {2, 3, 5, 7, 11, 13, 17, 19}
B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
𝜉 is all the numbers 1 to 20.
a) Find A ∩ B
b) Find A ∪ B
c) What would a Venn diagram look like?
A B
A ∪ B
A B
A ∩ B
𝜉
𝜉
A B
A’
A B
A ∩ B’
𝜉
𝜉
Example 2
The Venn diagram shows the number of people
who like Pepsi Max and Coke Zero.
P C
a) Find P(P)
b) Find P(P ∪ C)
c) Find P(P ∩ C’)
31 5 2
9 𝜉
Example 3
A B
a) Find P(A) b) Find P(A’ ∩ B’)
c) Find P(A’ ∩ B)
d) Are A and B independent?
0.5 0.1 0.2
0.2 𝜉
If A and B are independent then the outcome of one
event doesn’t affect the probability of the other and
P(A) x P(B) = P(A ∩ B)
Example 4
P(A) = 0.25, P(B) = 0.6 and P(A ∩ B) = 0.05.
a) Draw a Venn diagram
b) Find P(A ∪ B)
c) Find P(A’ ∩ B)
d) Are A and B mutually exclusive?
If A and B are mutually exclusive then the events
cannot happen at the same time.
P(A ∩ B) = 0

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Set-notation--venn-diagrams-and-probability [Read-Only].pptx

  • 1. Lets talk about Definition: A set is a collection of objects named elements. Notation: A set can be defined by listing its elements between braces. Example: A = {1, 2, 3, 4, 5}.   If something is an element of a set we use . If something is not an element we use . Example: , . A 89 A 2  
  • 2. Lets talk about If a set has no elements it is called the empty set. It is written as ∅. The universal set is the set of all elements being considered. It is written 𝜉.
  • 3. Lets talk about The union of two sets, A and B, is the elements in A or B or in both. It is written A ∪ B.  The intersection of two sets, A and B, is the elements that are in A and B. It is written A ∩ B.
  • 4. Example 1 A = {2, 3, 5, 7, 11, 13, 17, 19} B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} 𝜉 is all the numbers 1 to 20. a) Find A ∩ B b) Find A ∪ B c) What would a Venn diagram look like?
  • 5. A B A ∪ B A B A ∩ B 𝜉 𝜉
  • 6. A B A’ A B A ∩ B’ 𝜉 𝜉
  • 7. Example 2 The Venn diagram shows the number of people who like Pepsi Max and Coke Zero. P C a) Find P(P) b) Find P(P ∪ C) c) Find P(P ∩ C’) 31 5 2 9 𝜉
  • 8. Example 3 A B a) Find P(A) b) Find P(A’ ∩ B’) c) Find P(A’ ∩ B) d) Are A and B independent? 0.5 0.1 0.2 0.2 𝜉 If A and B are independent then the outcome of one event doesn’t affect the probability of the other and P(A) x P(B) = P(A ∩ B)
  • 9. Example 4 P(A) = 0.25, P(B) = 0.6 and P(A ∩ B) = 0.05. a) Draw a Venn diagram b) Find P(A ∪ B) c) Find P(A’ ∩ B) d) Are A and B mutually exclusive? If A and B are mutually exclusive then the events cannot happen at the same time. P(A ∩ B) = 0