Venn and Tree Diagrams

Probability

Tree diagrams

With replacement

Finding probability

Remember to multiply as you walk along the branches of the tree diagram

Multiple Choice

Two dice are rolled and it is recorded whether the result on each is odd or even. What is the probability both are odd?

• 1/4

• 1/2

• 2/4

• 3/4

Multiple Choice

What is the chance that the dessert is not brownies and does not have peanut butter in it?

• 0.58

• 0.42

• 0.06

• 0.05

Multiple Choice

What is the probability the dessert has peanut butter in it?

• 0.84

• 0.58

• 0.22

• 0.59

Multiple Choice

What is the probability of spinning an even number? 

• equally likely
• very likely 
• certain
• impossible 

Multiple Choice

Use the tree diagram to find the probability of tossing a head first and then a tail when a coin is tossed twice.

• 1

• 1_/2

• 1/₄

• 1/8

Tree diagrams

Without replacement

Multiple Choice

There are 10 counters in a bag, 3 red and 7 blue.

I take one counter, then another without replacement.

Find the probability of the value marked x

• ⁷/₁₀

• ³/₁₀

• ⁶/₉

• ²/₉

Multiple Choice

There are 10 counters in a bag, 3 red and 7 blue.

I take one counter, then another without replacement.

Find the probability of the value marked y

• ⁷/₁₀

• ³/₁₀

• ⁶/₉

• ²/₉

Multiple Choice

There are 10 counters in a bag, 3 red and 7 blue.

I take one counter, then another without replacement.

Find the probability of picking one of each colour counters.

• ²¹/₉₀

• ⁴⁸/₉₀

• ⁴²/₉₀

• ¹⁰/₁₉

Venn diagrams

 $P\left(A\cup B\right)$  
 $P\left(A\cap B\right)$  
 $P\left(A'\right)$   

Venn diagrams

 $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$  

Number of 
elements

 $n\left(A\right)=$  

 $n\left(A\cap B\right)=$  

3 Set Venn diagrams

Multiple Choice

The venn diagram shows which sports are played by a class of students.

How many students are in the class?

• 20

• 25

• 30

• 35

Multiple Choice

The venn diagram shows which sports are played by a class of students.

What is the probability of a student playing both tennis soccer?

• 1/6

• 5

• 20

• 2/3

Multiple Choice

The venn diagram shows which sports are played by a class of students.

What is the probability of a student playing tennis or soccer?

• 1/6

• 5

• 20

• 2/3

Multiple Choice

The venn diagram shows which sports are played by a class of students.

What is the probability of a student playing neither tennis nor soccer?

• 1/3

• 10

• 20

• 2/3

Multiple Choice

The venn diagram shows the number of people in a group of friends who have brown hair and green eyes.

How many friends are in the group?

• 11

• 6

• 12

• 7

Multiple Choice

The venn diagram shows the number of people in a group of friends who have brown hair and green eyes.

What is the probability of a friend having brown hair?

• 3

• 1

• 4

• 4/11

Multiple Choice

The venn diagram shows the number of people in a group of friends who have brown hair and green eyes.

What is the probability of a friend having neither brown hair nor green eyes?

• 7/11

• 5/11

• 6/11

• 3/11

Multiple Choice

The venn diagram shows the number of students in chorus, band, and/or orchestra.

What is the probability that a student is in both chorus and band?

• 9/70

• 9/54

• 9/37

• 5/54

Multiple Choice

The venn diagram shows the number of students in chorus, band, and/or orchestra.

How many students are in chorus, band, and orchestra?

• 5

• 9

• 24

• 15

Multiple Choice

The venn diagram shows the number of students in chorus, band, and/or orchestra.

How many students are in the orchestra?

• 16

• 21

• 31

• 36

Multiple Choice

The venn diagram shows the number of students in chorus, band, and/or orchestra.

What is the probability that a student is in the chorus but not the orchestra?

• 10/70

• 14/70

• 14/50

• 10/50