12.3

PROBABILTY WITH

VENN DIAGRAMS

MDM

Objectives

Calculate probability involving “not”, “and”, “or”

Use tables and Venn diagrams to calculate probabilities

Probability Notation

𝑃 𝐴

𝑃(ഥ𝐴 )

𝑃 𝐴 ∩ 𝐵

𝑃(𝐴 ∪ 𝐵)

Probability Notation

𝑃 𝐴 Probability of A occurring

𝑃(ഥ𝐴 ) Probability of A NOT occurring

𝑃 𝐴 ∩ 𝐵 Probability of both A AND B occurring

𝑃(𝐴 ∪ 𝐵) Probability of either A OR B occurring

Probability Notation

Ex 1: You have a list of five names: Alicia, Brita, Steve, Don, Ellis

B: name begins with a vowel E: name ends with a vowel

A. 𝑃 𝐵

B. 𝑃( ഥ𝐵 )

C. 𝑃 𝐵 ∩ 𝐸

D. 𝑃(𝐵 ∪ 𝐸)

Probability Notation

A. 𝑃 𝐵2

5= 0.4 = 40%

B. 𝑃( ഥ𝐵 )3

5= 0.6 = 60%

C. 𝑃 𝐵 ∩ 𝐸1

5= 0.2 = 20%

D. 𝑃(𝐵 ∪ 𝐸)4

5= 0.8 = 80%

Venn Diagram

Ex 2: A group of students were surveyed.

A. How many students were asked?

B. What were they asked?

C. What does 375 represent?

Venn Diagram

Ex 2: A group of students were surveyed.

A. How many students were asked? 1000

B. What were they asked? Band or Choir

C. What does 375 represent? Neither

Venn Diagram

Ex 2: A group of students were surveyed.

D. P(choir)

E. P(choir ∩ band)

F. P(choir ∪ band)

Venn Diagram

Ex 2: A group of students were surveyed.

D. P(choir) 400

1000=

2

5= 0.4 = 40%

E. P(choir ∩ band) 50

1000=

1

20= 0.05 = 5%

F. P(choir ∪ band) 675

1000=

5

8= 0.625 = 62.5%

Venn Diagram

Ex 3: 200 students were asked whether they get help during SKYtime or after school. 75 get help during both times, 100 said they get help after school, and 30 said neither.

Complete the Venn Diagram.

Venn Diagram

Ex 3: 200 students were asked whether they get help during SKYtime or after school. 75 get help during both times, 100 said they get help after school, and 30 said neither.

Complete the Venn Diagram.

SKYtime

70

After

School

2575

30

Venn Diagram

Ex 4: Use your Venn Diagram to answer the questions:

A. P(ST)

B. P(AS)

C. P(𝐴𝑆)

D. P(ST ∪ AS)

SKYtime

70 75

After

School

25

30

Venn Diagram

A. P(ST) 145

200=

29

40= 0.725 = 72.5%

B. P(AS) 100

200=

1

2= 0.5 = 50%

C. P(𝐴𝑆)100

200=

1

2= 0.5 = 50%

D. P(ST ∪ AS) 170

200=

34

40= 0.85 = 85%

SKYtime

70 75

After

School

25

30

Two Way Tables

Ex 5: Do people find greater

stress relief from throwing things

or screaming loudly?

A. P(Throwing)

B. P(Feel better)

C. P(Screaming ∩ Feel better)

Feel Better

Don’t Feel Better

Total

Throwing things

112 28 140

Screaming loudly

224 56 280

Total 336 84 420

Two Way Tables

A. P(Throwing) 140

420=

1

3= 0.33 = 33%

B. P(Feel better) 336

420=

4

5= 0.8 = 80%

C. P(Screaming ∩ Feel better)

224

420=

8

15= 0.53 = 53.3%

Feel Better

Don’t Feel Better

Total

Throwing things

112 28 140

Screaming loudly

224 56 280

Total 336 84 420

HOMEWORK

Assignment 12.2

EDPuzzle 12.2