Sample Space Venn Diagram

Sets Venn Diagram

by MRS. MILLER-CAMPBELL

​What are sets?

​A set is a collection of elements that have certain things in common.

Multiple Choice

What is the meaning of the term set?

• a bag

• a collection of distinct elements  that have something in common.

• a member of a group

• several different things

​The Venn Diagram

​ A Venn diagram shows the relationships of different sets in a visual way

​Let's examine these Venn diagrams.

​

Multiple Choice

What are the two sets in the Venn diagram?

• superman & Flash

• Thor and Batman

• Super heroes with cape & Super heroes with dead parents.

• Green superheroes and pink super heroes.

Set (Venn Diagram) Language

Commonly sets interact. For example, you and a friend decide to have a party, and you both invite your circle of friends. At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets.​

​We use to terms

1. 1. union

2. 2. intersection

3. 3. complement

4. to show these comparisons

​The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.

Multiple Choice

What is the intersection of sets A and B?

A ⋂ B = ______

• 1, 2, 3, 4. 5

• 1, 2

• 3, 4, 6, 8

• 3, 4

Multiple Choice

Which colour is the intersection?

• blue

• green

• yellow

• red

​The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B.

Multiple Choice

What numbers or elements is complement of set A (A')

• 1, 3, 5

• 2, 4, 6

• 1, 2, 3, 4, 5, 6,

• 2, 4

Multiple Choice

A ' is ___________________

• Pentagon

  Hexagon

  octagon

• Nanogon 

  Heptagon

• Heptagon

• Pentagon

  Nanogon

  Hexagon

  Octagon

  Heptogon

Multiple Choice

Let the universal set, U = {a, e, i, o, u} and set A = {a, e}, then complement of set A is:

• {i, o, u}

• {a. i}

• {a. o}

• {a, u}

Venn Diagram

Objectives

Learning Objective: Students will construct Venn diagrams to determine probabilities of compound events.

Language Objective: Students will express their reasoning in written form.

Vocabulary

Venn Diagrams – visual way to divide up multiple categories

Intersection

In the Venn Diagram, the intersection is located in the middle.

​

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Union

In a Venn Diagram, the union is both circles shaded in.

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Find Probability

The following Venn diagram is a survey of students in Mrs. Tucker’s class that is taking art, band, or chemistry.

Multiple Choice

The diagram shows the sports played by 80 students.

If a student is picked at random, what is the probability that they play Hockey and Rugby?

• ³⁶/₈₀

• ⁵/₈₀

• ⁴¹/₈₀

• ⁴⁴/₈₀

Multiple Choice

The diagram shows the sports played by 80 students.

If a student is picked at random, what is the probability that they don't play any of the three sports?

• ⁷⁹/₈₀

• ¹/₈₀

• ⁷⁴/₈₀

• ⁶/₈₀

Multiple Choice

The diagram shows the sports played by 80 students.

If a student is picked at random, what is the probability that they play Rugby or Hockey?

• ⁷⁵/₈₀

• ⁸/₈₀

• ¹³/₈₀

• ⁴⁴/₈₀

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

The list of all possible outcomes is called the SAMPLE SPACE.

​

Probability is often defined as how likely something is to happen.

​Concept and Notations

​•The total U {Universal}?: Total number (Sum all up)

Multiple Choice

P(A) = ?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Multiple Choice

P(B) =?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Multiple Choice

P(A $$\cap$$  B) =?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Multiple Choice

P(A $$\cup$$  B) =?

• (5)/27

• (5+9)/27

• (5+7)/27

• (5+7+9)/27

Multiple Choice

Sample space is defined as...

• the likelihood of an event occurring.

• a diagram of all possible outcomes.

• the probability of an event.

• a list of all possible outcomes.