Simple Probability Diagrams (Edexcel GCSE Maths: Foundation)

Exam Questions

1 hour22 questions
1a
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3 marks

A cat rescue centre has 20 cats. There are male and female cats, and they are either long-haired or short-haired.

Complete the missing information in the two-way table below.

  Long Short Total
Male   10  
Female 3    
Total   12 20
1b
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1 mark

One of the cats is chosen at random.

Write down the probability that this cat is a female, long-haired cat.

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2a
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3 marks

A zoo has a colony of 75 penguins.

There are two species; emperor penguins and king penguins.

The penguins are either adults or chicks.

20 of the 48 adults are emperor penguins.

15 of the chicks are king penguins.

Use this information to complete the frequency tree.

Frequency tree diagram

2b
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1 mark

One of the penguins is selected at random.

Find the probability that this penguin is an adult king penguin.

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3
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3 marks

A bird watcher makes the following frequency tree for male and female ducks and swans that they spot on their local duck pond.

Frequency tree diagram showing the number of male and female ducks and swans on a pond

Use the frequency tree to complete the two-way table.

  Duck Swan Total
Male      
Female      
Total      

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4
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2 marks

Use set notation to describe the shaded region in each Venn diagram.

qp9a-0580-31-paper-3-may-2020-cie-igcse-maths

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5a
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1 mark

qp16a-0580-12-paper-1-may-2020-cie-igcse-maths

On the Venn diagram, shade the region A intersection B.

5b
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2 marks

calligraphic E = {1, 2, 3, 4, 5, 6}
P= {x : x is an even number}
Q = {x : x is a prime number}

qp16b-0580-12-paper-1-may-2020-cie-igcse-maths

Complete the Venn diagram.

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6a
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1 mark

Use set notation to describe the shaded regions in each Venn diagram.

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6b
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1 mark

qp20b-0580-01-paper-1-specimen-2020-cie-igcse-maths

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1a
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3 marks

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.

  Dog Cat Total
Black      
White      
Total      
1b
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1 mark

A cat is selected at random.

Write down the probability of the cat being white.

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2a
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3 marks

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.

Incomplete frequency tree diagram for the number of males and females that like or do not like tea

2b
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1 mark

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

Find the probability that this person is a woman.

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3
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3 marks

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.

  Within speed limit Over speed limit Total
Car 25   33
Van     15
Total 35 13  

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

Incomplete frequency tree diagram for the number of cars and vans on a road that are travelling within the speed limit or over the speed limit

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4
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3 marks
i)
calligraphic E= {2, 4, 8, 16, 32, 64}
A = {square numbers}
B = {cube numbers}


Use this information to complete the Venn diagram.

qp3di-0580-31-paper-3-nov-2020-cie-igcse-maths

[2]

ii)
On this Venn diagram, shade the region P union Q.
qp3dii-0580-31-paper-3-nov-2020-cie-igcse-maths
[1]

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5
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3 marks

In a group of 40 students,

  • 24 students like football
  • 19 students like cricket
  • 10 students like football but not cricket.

qp8c-0580-32-paper-3-nov-2020-cie-igcse-maths

Complete the Venn diagram.

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6a
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2 marks

calligraphic E = {children in a group}
R space= {children who own a rabbit}
H = {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.

qp21a-0580-13-paper-1-nov-2020-cie-igcse-maths

6b
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1 mark

Write down n open parentheses R intersection H close parentheses.

[1]

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7
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5 marks

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

qp5a-0580-33-paper-3-may-2020-cie-igcse-maths

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  n open parentheses A union B close parentheses.
[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]

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8
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7 marks

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

  Adult Child Total
Male   144 240
Female 129   260
Total 225 275 500

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]

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1a
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3 marks

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.

  Giraffes Zebras Total
Male      
Female      
Total      

 

1b
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2 marks

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?

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2a
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3 marks

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.

Empty frequency tree diagram for the number of households with or without pets and with or without children

2b
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1 mark

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.

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3
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4 marks

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.

Frequency tree diagram for the number of fish that are Goldfish or Koi and are orange or white in colour

 

  Orange White Total
Goldfish   8  
Koi      
Total     29

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4
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6 marks

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

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i)
Write down straight n open parentheses A close parentheses.

[1]

ii)
List the elements of set B.
B space= { ............................................... } [2]
One of these 19 numbers is picked at random.


Work out the probability that this number is

iiia)
not in set A and not in set B,
[1]
iiib)
in A union B
[1]

iv)
Complete the statement.

A intersection B equals open curly brackets x space colon space x space is space............................... close curly brackets

[1]

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5
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2 marks

calligraphic E = {x : x is a natural number less-than or slanted equal to15}
F = {x : x is a factor of 12}
O = {x : x is an odd number}

i)
Complete the Venn diagram to show the elements of these sets.
qp9b-0580-31-paper-3-may-2020-cie-igcse-maths
[2]
ii)
Write down one number that is in set O, but not in set F.
[1]
iii)
Find straight n open parentheses F union O close parentheses.
[1]
iv)
A number is chosen at random from calligraphic E.
Work out the probability that this number is in set O.
[1]

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6
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9 marks

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

i)
Write down the elements in set F.
F = { ................................................ } [2]
 
ii)
Write down the elements in set P.
P = { ................................................ } [2]
 

qp9aiii-0580-32-paper-3-march-2020-cie-igcse-maths

iiia)
Complete the Venn diagram.
[2]
 
iiib)
Write down  straight n(F intersection P)
[1]
 
iiic)
A number is chosen at random from the universal set calligraphic E.

Write down the probability that the number is in the set  F space union P .
[2]

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7a
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2 marks

calligraphic E= {children who go to the park}
space T space= {children who play tennis}
G = {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.

qp23a-0580-01-paper-1-specimen-2020-cie-igcse-maths

[2]

7b
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1 mark

Find n(T space intersection space G).

[1]

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8a
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3 marks

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

  French German Spanish Italian Japanese Total
Boys 27   48 19   123
Girls   32 54   12  
Total   53   30   262

Complete the table.

[3]

8b
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3 marks

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]

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