Basic Probability and Venn Diagrams

Venn Diagram Notes

Objectives

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

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

Warm Up

Write each number in scientific notation.
1) 0.000325 =
2) 56,000,000 =

Write each number in standard notation.

3) $3.0\times10^{-1}$  

4) $1.2\times10^3$  

Multiple Choice

Write the following number in scientific notation.

0.00023 =

• $$2.3\times10^4$$

• $$2.3\times10^{-4}$$

• $$2.3\times10^5$$

• $$2.3\times10^{-5}$$

Multiple Choice

Write the following number in scientific notation.

21,000 =

• $$2.1\times10^4$$

• $$2.1\times10^{-4}$$

• $$2.1\times10^5$$

• $$2.1\times10-5$$

Multiple Choice

Write each number in standard notation.

$$2.0\times10^4$$  

• .002

• .0002

• 2,000

• 20,000

Multiple Choice

Write the following number in standard notation.

$$5.0\times10^{-2}$$  

• 0.5

• 0.05

• 50

• 500

Vocabulary

Venn Diagrams – visual way to divide up multiple categories

Intersection

Intersection: is when both events occurs. It is the overlapping of the events.
Notation: 

  $P\left(A\ and\ B\right)$  
 $P\left(A\cap B\right)$  
Remember: (Intersection = AND)

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

Union

Union: is when A, B or BOTH events occur.
It is the probability of getting at least one of the events or both or the other event.

Notation:

 $P\left(A\ or\ B\right)$  
 $P\left(A\cup B\right)$  
Remember: (Union = OR)

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

Find Probability

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

Find Probability Examples:

A) What is the total number of students in Mrs. Tucker’s class?

B) What is the probability that Mrs. Tucker’s students are in art and band?

C) What is the probability that Mrs. Tucker’s students are band?

D) What is the probability of Mrs. Tucker’s students not 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

Creating Venn Diagrams:

Draw a Venn diagram for the following:

A guidance counselor is planning schedules for 30 students. Sixteen students say they want to take French, 16 want to take Spanish, and 11 want to take Latin. Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish. How many students want French only?

Shading Venn Diagrams:

A) (𝐴 ∩ 𝐵)  

B) 𝐴 ∪ B

C) 𝐴 ∩ (𝐵 ∪ 𝐶)

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

End of the Lesson

Homework Due on Friday