Simple Probability Diagrams (Edexcel GCSE Maths: Foundation)

A veterinary centre tracks the number of black and white cats and dogs who enter the practice on a particular day.

14 are counted in total.

6 of these are dogs.

4 of the dogs are black.

There is 1 white cat.

Use this information to complete the two-way table.

A cat is selected at random.

Write down the probability of the cat being white.

A survey is taken in an office to see how many staff like to drink tea.

70 staff are asked in total.

42 of these people are women.

49 of the 70 staff like to drink tea.

10 of the men do not like to drink tea.

Use this information to complete the frequency tree.

One of the people who like to drink tea is chosen at random.

Find the probability that this person is a woman.

A police officer is checking if cars and vans on a particular road are driving within the speed limit, or over the speed limit.

The police officer produces the following two-way table which is incomplete.

  By using the two-way table to help you, fill in the frequency tree below.

i) = {2, 4, 8, 16, 32, 64}
= {square numbers}
= {cube numbers}

Use this information to complete the Venn diagram.

[2]

ii) On this Venn diagram, shade the region .

[1]

In a group of 40 students,

• 24 students like football

• 19 students like cricket

• 10 students like football but not cricket.

Complete the Venn diagram.

 = {children in a group}
= {children who own a rabbit}
= {children who own a hamster}

There are 40 children in the group.
19 children own a rabbit.
27 children own a hamster.

Complete the Venn diagram.

Write down

[1]

The Venn diagram shows information about the number of students in a class who like apples () and bananas ().

i) Work out the number of students in the class.

[1]

ii) Work out the number of students who like bananas.

[1]

iii) Work out  .

[1]

iv) How many more students like apples than like bananas?

[1]

v) One of the students is chosen at random.

Find the probability that this student does not like apples and does not like bananas.

[1]

The table gives some information about the numbers of visitors at a leisure centre one day.

i) Complete the table.

[1]

ii) Work out how many more child visitors than adult visitors there are.

[1]

iii) Write down the fraction of visitors that are adults.
Give your answer in its lowest terms.

[2]

iv) Write the ratio number of males : number of females.
Give your answer in its simplest form.

..................... : ................... [2]

v) One of these visitors is selected at random.
Find the probability that this visitor is a male child.

[1]

A group of conservationists note the numbers of male and female giraffes and zebras they see while on safari.

They spot 28 giraffes and zebras in total.

12 of these are female zebras.

They also spot 2 male giraffes.

The conservationists note that they saw 4 times more male zebras than male giraffes.

Use this information to fill in the two-way table.

The conservationists find a large herd of 100 zebras.

Using the data in part (a), how many of these 100 zebras are expected to be female?

There are 180 households in a village.

70 households do not have a pet.

45 households do not have a pet, and do not have children either.

There are 105 households who have children.

Use this information to complete the frequency tree.

One of the households in the village is picked at random.

Find the probability of the household having either:    
no pets and no children    
or    
having both pets and children.

Naomi and Jamie own a fish pond that contains two types of fish: Goldfish and Koi.

The Goldfish and Koi are either orange or white in colour.

Jamie starts to create a frequency tree of the fish, and Naomi starts to create a two-way table of the fish.

Both of their incomplete diagrams are shown below.

Complete both diagrams.

 = { : is a positive integer less than 20}
A = { : is an even number}
B = { : is a multiple of 3}

i) Write down .

[1]

ii) List the elements of set .

= { ............................................... } [2]

One of these 19 numbers is picked at random.

Work out the probability that this number is

iiia) not in set and not in set ,

[1]

iiib) in

[1]

iv) Complete the statement.

[1]

 = { : is a natural number 15}
= { : is a factor of 12}
= { : is an odd number}

i) Complete the Venn diagram to show the elements of these sets.

[2]

ii) Write down one number that is in set , but not in set .

[1]

iii) Find .

[1]

iv) A number is chosen at random from .

Work out the probability that this number is in set .

[1]

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} = {: is a factor of 14} = {: is a prime number less than 14}

i) Write down the elements in set .

= { ................................................ } [2]

 ii) Write down the elements in set .

= { ................................................ } [2]

iiia) Complete the Venn diagram.

[2]

iiib) Write down  ()

[1]

 iiic) A number is chosen at random from the universal set .

Write down the probability that the number is in the set  .

[2]

= {children who go to the park}
= {children who play tennis}
= {children who play golf}

120 children go to the park.
50 play tennis.
75 play golf.
25 do not play tennis or golf.

Complete the Venn diagram.

Find n().

[1]

The 262 students at a college each study one of the languages shown in the table.

Complete the table.

[3]

Find the probability that

i) a girl, chosen at random, studies Spanish,

[1]

ii) a boy, chosen at random, studies French or Italian,

[1]

iii) a student, chosen at random, does not study German.

[1]