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Two-Way Tables (Cambridge (CIE) IGCSE International Maths)

Revision Note

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Cambridge (CIE) International Maths: CoreEdexcel Maths A (Modular): Higher Unit 2Cambridge (CIE) International Maths: ExtendedCambridge (CIE) Maths: CoreCambridge (CIE) Maths: ExtendedEdexcel Maths A: Higher

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Two Way Tables

What are two-way tables?

  • Two-way tables are tables that compare two types of characteristics

    •  For example, a college of 55 students has two year groups (Year 12 and Year 13) and two language options (Spanish and German)

    • The two-way table is shown: 

       

      Spanish

      German

      Year 12

      15

      10

      Year 13

      5

      25

How do I find probabilities from a two-way table?

  • Draw in the totals of each row and column

    • Include an overall total in the bottom-right corner

      • It should be the sum of the totals above, or to its left (both work)

    • For the example above:
       

       

      Spanish

      German

      Total

      Year 12

      15

      10

      25

      Year 13

      5

      25

      30

      Total

      20

      35

      55

  • Use this to answer probability questions

    • If a random student is selected from the whole college, it will be out of 55

      • The probability a student selected from the college studies Spanish and is in Year 12 is 15 over 55

      • The probability a student selected from the college studies Spanish is 20 over 55

    • If a random student is selected from a specific category, the denominator will be that category total

      • The probability a student selected from Year 13 studies Spanish is 5 over 30

Examiner Tips and Tricks

  • Check your row and column totals add up to the overall total, otherwise all your probabilities will be wrong!

Worked Example

At an art group, children are allowed to choose between colouring, painting, clay modelling and sketching.

A total of 60 children attend and are split into two classes: class A and class B.
12 of class A chose the activity colouring and 13 of class B chose clay modelling.
A total of 20 children chose painting and a total of 15 chose clay modelling.
8 of the 30 children in class A chose sketching, as did 4 children in class B.

 (a) Construct a two-way table to show this information.

Read through each sentence and fill in the numbers that are given

 

Colouring

Painting

Clay modelling

Sketching

Total

Class A

12

 

 

8

30

Class B

 

 

13

4

 

Total

 

20

15

 

60

Use the row and column totals to fill in any obvious missing numbers

 

Colouring

Painting

Clay modelling

Sketching

Total

Class A

12

 

15 - 13 = 2

8

30

Class B

 

 

13

4

60 - 30 = 30

Total

 

20

15

8 + 4 = 12

60

Use the row and column totals again to find the last few numbers

 

Colouring

Painting

Clay modelling

Sketching

Total

Class A

12

30 - 12 - 2 - 8 = 8

2

8

30

Class B

30 - 12 - 13 - 4 = 1

20 - 8 = 12

13

4

30

Total

12 + 1 = 13

20

15

12

60

Write out your final answer

 

Colouring

Painting

Clay modelling

Sketching

Total

Class A

12

8

2

8

30

Class B

1

12

13

4

30

Total

13

20

15

12

60

(b) Find the probability that a randomly selected child

(i) chose colouring,

(ii) is in class A, who chose sketching.

(i) We are not interested in whether the child is in class A or B
A total of 13 children chose colouring, out of 60 children

P(colouring) = 13 over 60

(ii) 8 children in class A chose sketching
There are 60 children to select from

P(class A and sketching) = 8 over 60 equals 2 over 15

(c) A child in class B is selected at random. Find the probability they chose painting.

As we are only selecting from class B, this will be out of 30 (rather than the total of 60)
12 in class B chose painting

P(painting, from class B only) = 12 over 30 equals 2 over 5 

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    Author
    Reviewer
    Mark Curtis

    Author: Mark Curtis

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.