Venn Diagrams

More Venn Diagrams

Objectives:

Learning Objective: Students will use Venn Diagrams to determine risk.

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

Vocabulary:

The complement of an event is a way of saying not. It’s the probability of an event not happening.

We use the symbols ' or - or ^c to represent an intersection. We use the word not to explain an intersection.

Example: P(A u B)'

This means NOT A or B, in other words every event where A, B, both don’t happen.

Notice, the shading did not includes circle A or circle B.

Examples:

Draw a Venn Diagram for the following situation and then answer the questions about the probabilities. 27% of the ice creams in the freezer at dairy mart are Popsicle, 35% of the ice creams are chocolate flavor, 15% are chocolate Popsicle.

a) P(Popsicle)

b) P(Popsicle)'

c) P(Popsicle u Chocolate)

d) P(Popsicle n Chocolate)

e) P(Popsicle u Chocolate)'

Multiple Choice

At Ridgemont High school, there are 150 seniors, 70 own dogs, 30 own cats, and 25 own both. Reduce you answer.
Find

$$P\left(Cat\ \cap Dog\right)$$  

• $$\frac{1}{30}$$  

• $$\frac{1}{6}$$  

• $$\frac{3}{10}$$  

• $$\frac{1}{2}$$  

Multiple Choice

At Ridgemont High school, there are 150 seniors, 70 own dogs, 30 own cats, and 25 own both. Reduce you answer. 
Find

$$P\left(Cat\ \cup Dog\right)$$  

• $$\frac{1}{30}$$  

• $$\frac{1}{6}$$  

• $$\frac{3}{10}$$  

• $$\frac{1}{2}$$  

Multiple Choice

At Ridgemont High school, there are 150 seniors, 70 own dogs, 30 own cats, and 25 own both.  Reduce you answer.
Find

$$P\left(Cat\ \cup Dog\right)'$$  

• $$\frac{1}{30}$$  

• $$\frac{1}{6}$$  

• $$\frac{3}{10}$$  

• $$\frac{1}{2}$$  

Example: Shading Venn Diagrams:

1) Shade A'
2) Shade  $\left(A\cap B\right)$  

3) Shade  $\left(A\cap B\right)'$  

Multiple Choice

Identify the shaded area...

• A∩B

• A∪B

• A'∩B'

• A'∪B'

Multiple Choice

Identify the shaded area...

• A

• B

• A'

• B'

Formulas:

To find a union (or) mathematically we use the equation:
 $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$  
To find a compliment mathematically we use the equation:
 $P\left(A\right)'=1-P\left(A\right)$  

Example: Addition Rule

A new donut shop in town is trying to figure out what items will sell the most. Throughout their research of local donut shops, they have

found that 63% of customers purchase a donut, 80% of people purchased coffee and 88% of people purchase a coffee or a donut. They want to know what percent of people purchased a coffee and a donut.

Multiple Choice

Thirty-two percent of families residing in a rural, farming town own a goat and 41% of families own a dog. Twenty-four percent of families own both types of animals. If a family from this town is chosen at random, what is the probability that it owns either a goat or a dog?

• 0.15

• 0.33

• 0.49

• 0.97

Multiple Choice

The probability of a New York teenager owning a skateboard is 0.37, of owning a bicycle is 0.81 and of owning both is 0.36. If a New York teenager is chosen at random, what is the probability that the teenager owns a skateboard or a bicycle?

• 1.18

• 0.7

• 0.82

• None of the above

Example: Compliment

1) What is the compliment of flipping a coin 20 times and landing on heads 11 times?

2) What is the compliment of drawing a green marble, if there are 10 green marbles in a jar with 15 marbles?

Multiple Choice

What is the complement of it snowing 3 days out of the week?

• P' = 4/7

• P' = 2/7

• P' = 5/7

• P' = 3/7

Multiple Choice

How likely are you to NOT roll a 1 on a regular die? (Complement)

• P' = 2/6

• P' = 3/6

• P' = 5/6

• P' = 1/6

End of Lesson

Remember: Homework due on Monday.